Real Homotopy Of Configuration Spaces

Author : Najib Idrissi
Publisher : Springer Nature
Page : 201 pages
File Size : 54,9 Mb
Release : 2022-06-11
Category : Mathematics
ISBN : 9783031044281

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Real Homotopy of Configuration Spaces by Najib Idrissi Pdf

This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds. Configuration spaces consist of collections of pairwise distinct points in a given manifold, the study of which is a classical topic in algebraic topology. One of this theory’s most important questions concerns homotopy invariance: if a manifold can be continuously deformed into another one, then can the configuration spaces of the first manifold be continuously deformed into the configuration spaces of the second? This conjecture remains open for simply connected closed manifolds. Here, it is proved in characteristic zero (i.e. restricted to algebrotopological invariants with real coefficients), using ideas from the theory of operads. A generalization to manifolds with boundary is then considered. Based on the work of Campos, Ducoulombier, Lambrechts, Willwacher, and the author, the book covers a vast array of topics, including rational homotopy theory, compactifications, PA forms, propagators, Kontsevich integrals, and graph complexes, and will be of interest to a wide audience.

Author : Edward R. Fadell,Sufian Y. Husseini
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642564468

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Geometry and Topology of Configuration Spaces by Edward R. Fadell,Sufian Y. Husseini Pdf

With applications in mind, this self-contained monograph provides a coherent and thorough treatment of the configuration spaces of Euclidean spaces and spheres, making the subject accessible to researchers and graduates with a minimal background in classical homotopy theory and algebraic topology.

Author : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 52,5 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897

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Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo Pdf

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Author : Pavle V. M. Blagojević,Frederick R. Cohen,Michael C. Crabb,Wolfgang Lück,Günter M. Ziegler
Publisher : Springer Nature
Page : 217 pages
File Size : 41,6 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030841386

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Equivariant Cohomology of Configuration Spaces Mod 2 by Pavle V. M. Blagojević,Frederick R. Cohen,Michael C. Crabb,Wolfgang Lück,Günter M. Ziegler Pdf

This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(R^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F(R^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper. This invalidates a paper by three of the authors, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and l-skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker. Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry.

Author : Filippo Callegaro,Frederick Cohen,Corrado De Concini,Eva Maria Feichtner,Giovanni Gaiffi,Mario Salvetti
Publisher : Springer
Page : 379 pages
File Size : 55,7 Mb
Release : 2016-08-27
Category : Mathematics
ISBN : 9783319315805

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Configuration Spaces by Filippo Callegaro,Frederick Cohen,Corrado De Concini,Eva Maria Feichtner,Giovanni Gaiffi,Mario Salvetti Pdf

This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.

Author : Jaume Aguade,Carles Broto,Carles Casacuberta
Publisher : Birkhäuser
Page : 413 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883122

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Cohomological Methods in Homotopy Theory by Jaume Aguade,Carles Broto,Carles Casacuberta Pdf

This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca Matemtica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category. The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.

Author : Jean-Louis Loday
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 49,9 Mb
Release : 1997
Category : Electronic
ISBN : 9780821805138

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Operads: Proceedings of Renaissance Conferences by Jean-Louis Loday Pdf

Author : Haynes Miller
Publisher : CRC Press
Page : 982 pages
File Size : 49,9 Mb
Release : 2020-01-23
Category : Mathematics
ISBN : 9781351251617

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Handbook of Homotopy Theory by Haynes Miller Pdf

The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Author : V Arnold,M. Monastyrsky
Publisher : CRC Press
Page : 312 pages
File Size : 43,8 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0412452707

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Developments in Mathematics by V Arnold,M. Monastyrsky Pdf

A collection of seven survey articles especially commissioned by Professors Arnold and Monastyrsky highlighting areas where the Moscow scholl has amde significant recent contributions to theoretical mathematics. Contributions include papers on Knot theory, supersurfaces and dynamical systems. This book contains articles on aspects of mathematics that have become increasingly important in the west. The editors are internationally renowned for the standard of their work.

Author : Mahender Singh,Yongjin Song,Jie Wu
Publisher : Springer
Page : 313 pages
File Size : 49,7 Mb
Release : 2019-02-02
Category : Mathematics
ISBN : 9789811357428

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Algebraic Topology and Related Topics by Mahender Singh,Yongjin Song,Jie Wu Pdf

This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.

Author : Yves Félix,Gregory Lupton,Samuel B. Smith
Publisher : American Mathematical Soc.
Page : 246 pages
File Size : 55,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849293

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Homotopy Theory of Function Spaces and Related Topics by Yves Félix,Gregory Lupton,Samuel B. Smith Pdf

This volume contains the proceedings of the Workshop on Homotopy Theory of Function Spaces and Related Topics, which was held at the Mathematisches Forschungsinstitut Oberwolfach, in Germany, from April 5-11, 2009. This volume contains fourteen original research articles covering a broad range of topics that include: localization and rational homotopy theory, evaluation subgroups, free loop spaces, Whitehead products, spaces of algebraic maps, gauge groups, loop groups, operads, and string topology. In addition to reporting on various topics in the area, this volume is supposed to facilitate the exchange of ideas within Homotopy Theory of Function Spaces, and promote cross-fertilization between Homotopy Theory of Function Spaces and other areas. With these latter aims in mind, this volume includes a survey article which, with its extensive bibliography, should help bring researchers and graduate students up to speed on activity in this field as well as a problems list, which is an expanded and edited version of problems discussed in sessions held at the conference. The problems list is intended to suggest directions for future work.

Author : Anders Björner,Fred Cohen,Corrado De Concini,Claudo Procesi,Mario Salvetti
Publisher : Springer
Page : 547 pages
File Size : 49,9 Mb
Release : 2013-12-18
Category : Mathematics
ISBN : 9788876424311

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Configuration Spaces by Anders Björner,Fred Cohen,Corrado De Concini,Claudo Procesi,Mario Salvetti Pdf

These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May-June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians.

Author : Vladimir Dobrev
Publisher : Springer
Page : 614 pages
File Size : 55,6 Mb
Release : 2016-12-10
Category : Science
ISBN : 9789811026362

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.“div>This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Author : F. R. Cohen,T. J. Lada,P. J. May
Publisher : Springer
Page : 501 pages
File Size : 51,9 Mb
Release : 2007-01-05
Category : Mathematics
ISBN : 9783540379850

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The Homology of Iterated Loop Spaces by F. R. Cohen,T. J. Lada,P. J. May Pdf

Author : A. Jon Berrick
Publisher : World Scientific
Page : 414 pages
File Size : 50,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814291415

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Braids by A. Jon Berrick Pdf

Tutorial on the braid groups / Dale Rolfsen -- Simplicial objects and homotopy groups / Jie Wu -- Introduction to configuration spaces and their applications / Frederick R. Cohen -- Configuration spaces, braids, and robotics / Robert Ghrist -- Braids and magnetic fields / Mitchell A. Berger -- Braid group cryptography / David Garber