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Author : Anonim
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 50,5 Mb
Release : 1999
Category : Homotopy theory
ISBN : 0821855638
Author : James D. Stasheff,John McCleary
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 48,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809136
Since the work of Stasheff and Sugawara in the 1960s on recognition of loop space structures on $H$-spaces, the notion of higher homotopies has grown to be a fundamental organizing principle in homotopy theory, differential graded homological algebra and even mathematical physics. This book presents the proceedings from a conference held on the occasion of Stasheff's 60th birthday at Vassar in June 1996. It offers a collection of very high quality papers and includes some fundamental essays on topics that open new areas. It's features include: accessible to a broad audience interested in mathematics and physics; offers a comprehensive overview of Stasheff's work; and, contains papers on very current research topics, including operads, combinatorial polyhedra and moduli spaces.
Author : Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 49,7 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9780817647353
This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.
Author : D.B. Fuchs,O.Ya. Viro
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 41,5 Mb
Release : 2003-10-27
Category : Mathematics
ISBN : 3540519963
Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.
Author : Carlos Simpson
Publisher : Cambridge University Press
Page : 653 pages
File Size : 41,6 Mb
Release : 2011-10-20
Category : Mathematics
ISBN : 9781139502191
The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.
Author : D.B. Fuchs,O.Ya. Viro
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 43,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662105818
Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.
Author : Hiro Lee Tanaka
Publisher : Springer Nature
Page : 84 pages
File Size : 44,9 Mb
Release : 2020-12-14
Category : Science
ISBN : 9783030611637
This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields.
Author : Martin Markl,Steven Shnider,James D. Stasheff
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 48,5 Mb
Release : 2002
Category : Operads
ISBN : 9780821843628
Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.
Author : Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu
Publisher : Unknown
Page : 380 pages
File Size : 45,5 Mb
Release : 2011-03-30
Category : Electronic
ISBN : 0817672311
Author : Michael I. Monastyrsky
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 51,8 Mb
Release : 2009-06-08
Category : Mathematics
ISBN : 9780817647797
The significantly expanded second edition of this book combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter.
Author : Jean-Pierre Meyer
Publisher : American Mathematical Soc.
Page : 392 pages
File Size : 49,6 Mb
Release : 1999
Category : Homotopy theory
ISBN : 9780821810576
This volume presents the proceedings of the conference held in honor of J. Michael Boardman's 60th birthday. It brings into print his classic work on conditionally convergent spectral sequences. Over the past 30 years, it has become evident that some of the deepest questions in algebra are best understood against the background of homotopy theory. Boardman and Vogt's theory of homotopy-theoretic algebraic structures and the theory of spectra, for example, were two benchmark breakthroughs underlying the development of algebraic $K$-theory and the recent advances in the theory of motives. The volume begins with short notes by Mac Lane, May, Stasheff, and others on the early and recent history of the subject. But the bulk of the volume consists of research papers on topics that have been strongly influenced by Boardman's work. Articles give readers a vivid sense of the current state of the theory of "homotopy-invariant algebraic structures". Also included are two major foundational papers by Goerss and Strickland on applications of methods of algebra (i.e., Dieudonné modules and formal schemes) to problems of topology. Boardman is known for the depth and wit of his ideas. This volume is intended to reflect and to celebrate those fine characteristics.
Author : M. Monastyrsky
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 41,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489924032
''Intended mainly for physicists and mathematicians...its high quality will definitely attract a wider audience.'' ---Computational Mathematics and Mathematical Physics This work acquaints the physicist with the mathematical principles of algebraic topology, group theory, and differential geometry, as applicable to research in field theory and the theory of condensed matter. Emphasis is placed on the topological structure of monopole and instanton solution to the Yang-Mills equations, the description of phases in superfluid 3He, and the topology of singular solutions in 3He and liquid crystals.
Author : D.B. Fuchs,O.Ya. Viro
Publisher : Springer
Page : 258 pages
File Size : 49,6 Mb
Release : 2013-01-22
Category : Mathematics
ISBN : 3662105829
Two top experts in topology, O.Ya. Viro and D.B. Fuchs, give an up-to-date account of research in central areas of topology and the theory of Lie groups. They cover homotopy, homology and cohomology as well as the theory of manifolds, Lie groups, Grassmanians and low-dimensional manifolds. Their book will be used by graduate students and researchers in mathematics and mathematical physics.
Author : Vladimir G. Turaev
Publisher : European Mathematical Society
Page : 300 pages
File Size : 43,6 Mb
Release : 2010
Category : EMS tracts in mathematics
ISBN : 3037190868
Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on $2$-dimensional and $3$-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Muger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.
Author : Alexei Davydov,Michael Batanin,Amnon Neeman,Michael Johnson
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 44,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821839706
Category theory has become the universal language of modern mathematics. This book is a collection of articles applying methods of category theory to the areas of algebra, geometry, and mathematical physics. Among others, this book contains articles on higher categories and their applications and on homotopy theoretic methods. The reader can learn about the exciting new interactions of category theory with very traditional mathematical disciplines.