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Author : Robert R. Bruner,J. Peter May,James E. McClure,Mark Steinberger
Publisher : Springer
Page : 396 pages
File Size : 53,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540397786
Author : Robert R. Bruner,J. Peter May,James E. McClure
Publisher : Unknown
Page : 400 pages
File Size : 46,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662211041
Author : Andrew J. Blumberg,Teena Gerhardt,Michael A. Hill
Publisher : Cambridge University Press
Page : 441 pages
File Size : 52,7 Mb
Release : 2022-07-21
Category : Mathematics
ISBN : 9781009123297
A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.
Author : R. James Milgram,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 52,7 Mb
Release : 1978
Category : Mathematics
ISBN : 9780821814338
Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.
Author : Daniel G. Davis
Publisher : American Mathematical Soc.
Page : 268 pages
File Size : 43,7 Mb
Release : 2019-05-30
Category : Homotopy theory
ISBN : 9781470442446
This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday, held from July 17–21, 2017, at the University of Illinois at Urbana-Champaign, Urbana, IL. The articles cover a variety of topics spanning the current research frontier of homotopy theory. This includes articles concerning both computations and the formal theory of chromatic homotopy, different aspects of equivariant homotopy theory and K-theory, as well as articles concerned with structured ring spectra, cyclotomic spectra associated to perfectoid fields, and the theory of higher homotopy operations.
Author : Yurii G. Borisovich,A.M. Vershik,Yurii E. Gliklikh
Publisher : Springer
Page : 338 pages
File Size : 51,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540458944
Author : Jose L. Bueso,Pascual Jara,Blas Torrecillas
Publisher : Springer
Page : 343 pages
File Size : 53,8 Mb
Release : 2007-01-05
Category : Mathematics
ISBN : 9783540392781
The papers in this proceedings volume are selected research papers in different areas of ring theory, including graded rings, differential operator rings, K-theory of noetherian rings, torsion theory, regular rings, cohomology of algebras, local cohomology of noncommutative rings. The book will be important for mathematicians active in research in ring theory.
Author : John McCleary
Publisher : Cambridge University Press
Page : 579 pages
File Size : 42,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9780521567596
Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.
Author : J. Peter May
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 43,6 Mb
Release : 1975
Category : Classifying spaces
ISBN : 9780821818558
The basic theory of fibrations is generalized to a context in which fibres, and maps on fibres, are constrained to lie in any preassigned category of spaces [script capital] F. Then axioms are placed on [script capital] F to allow the development of a theory of associated principal fibrations and, under several choices of additional hypotheses on [script capital] F, a classification theorem is proven for such fibrations.
Author : Jérôme Scherer
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 44,5 Mb
Release : 2018-05-30
Category : Algebraic topology
ISBN : 9781470429119
This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in Saas-Almagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic -theory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology.
Author : Takeo Ohsawa,Norihiko Minami
Publisher : Springer Nature
Page : 438 pages
File Size : 52,6 Mb
Release : 2020-03-18
Category : Mathematics
ISBN : 9789811515880
This volume originated in the workshop held at Nagoya University, August 28–30, 2015, focusing on the surprising and mysterious Ohkawa's theorem: the Bousfield classes in the stable homotopy category SH form a set. An inspiring, extensive mathematical story can be narrated starting with Ohkawa's theorem, evolving naturally with a chain of motivational questions: Ohkawa's theorem states that the Bousfield classes of the stable homotopy category SH surprisingly forms a set, which is still very mysterious. Are there any toy models where analogous Bousfield classes form a set with a clear meaning? The fundamental theorem of Hopkins, Neeman, Thomason, and others states that the analogue of the Bousfield classes in the derived category of quasi-coherent sheaves Dqc(X) form a set with a clear algebro-geometric description. However, Hopkins was actually motivated not by Ohkawa's theorem but by his own theorem with Smith in the triangulated subcategory SHc, consisting of compact objects in SH. Now the following questions naturally occur: (1) Having theorems of Ohkawa and Hopkins-Smith in SH, are there analogues for the Morel-Voevodsky A1-stable homotopy category SH(k), which subsumes SH when k is a subfield of C?, (2) Was it not natural for Hopkins to have considered Dqc(X)c instead of Dqc(X)? However, whereas there is a conceptually simple algebro-geometrical interpretation Dqc(X)c = Dperf(X), it is its close relative Dbcoh(X) that traditionally, ever since Oka and Cartan, has been intensively studied because of its rich geometric and physical information. This book contains developments for the rest of the story and much more, including the chromatics homotopy theory, which the Hopkins–Smith theorem is based upon, and applications of Lurie's higher algebra, all by distinguished contributors.
Author : L. Gaunce Jr. Lewis,J. Peter May,Mark Steinberger
Publisher : Springer
Page : 548 pages
File Size : 45,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540470779
This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find many details of the theory worked out for the first time. More subtle constructions like smash products, function spectra, change of group isomorphisms, fixed point and orbit spectra are treated. While it is impossible to survey properly the material which is covered in the book, it does boast these general features: (i) a thorough and reliable presentation of the foundations of the theory; (ii) a large number of basic results, principal applications, and fundamental techniques presented for the first time in a coherent theory, unifying numerous treatments of special cases in the literature.
Author : Heinz Hopf
Publisher : Springer
Page : 192 pages
File Size : 40,5 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540394822
These notes consist of two parts: Selected in York 1) Geometry, New 1946, Topics University Notes Peter Lax. by Differential in the 2) Lectures on Stanford Geometry Large, 1956, Notes J.W. University by Gray. are here with no essential They reproduced change. Heinz was a mathematician who mathema- Hopf recognized important tical ideas and new mathematical cases. In the phenomena through special the central idea the of a or difficulty problem simplest background is becomes clear. in this fashion a crystal Doing geometry usually lead serious allows this to to - joy. Hopf's great insight approach for most of the in these notes have become the st- thematics, topics I will to mention a of further try ting-points important developments. few. It is clear from these notes that laid the on Hopf emphasis po- differential Most of the results in smooth differ- hedral geometry. whose is both t1al have understanding geometry polyhedral counterparts, works I wish to mention and recent important challenging. Among those of Robert on which is much in the Connelly rigidity, very spirit R. and in - of these notes (cf. Connelly, Conjectures questions open International of Mathematicians, H- of gidity, Proceedings Congress sinki vol. 1, 407-414) 1978, .
Author : Robert R. Bruner,John Rognes
Publisher : American Mathematical Society
Page : 690 pages
File Size : 50,5 Mb
Release : 2021-12-23
Category : Mathematics
ISBN : 9781470469580
The connective topological modular forms spectrum, $tmf$, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of $tmf$ and several $tmf$-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The $H$-infinity ring structure of the sphere and of $tmf$ are used to determine many differentials and relations.
Author : Carlos A. Berenstein
Publisher : Springer
Page : 369 pages
File Size : 49,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540478935