Homotopy Invariant Algebraic Structures on Topological Spaces
Author: J. M. Boardman
Publisher: Springer
Published: 2006-11-15
Total Pages: 268
ISBN-13: 3540377999
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Homotopy Invariant Algebraic Structures
Author: Jean-Pierre Meyer
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 392
ISBN-13: 082181057X
DOWNLOAD EBOOKThis 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.
Cohomology Operations and Applications in Homotopy Theory
Author: Robert E. Mosher
Publisher: Courier Corporation
Published: 2008-01-01
Total Pages: 226
ISBN-13: 0486466647
DOWNLOAD EBOOKCohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.
Algebraic Structures Up to Homotopy
Author: Ronald James Williams
Publisher:
Published: 1975
Total Pages: 148
ISBN-13:
DOWNLOAD EBOOKA Concise Course in Algebraic Topology
Author: J. P. May
Publisher: University of Chicago Press
Published: 1999-09
Total Pages: 262
ISBN-13: 9780226511832
DOWNLOAD EBOOKAlgebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
A Physicists Introduction to Algebraic Structures
Author: Palash B. Pal
Publisher: Cambridge University Press
Published: 2019-05-23
Total Pages: 717
ISBN-13: 1108492207
DOWNLOAD EBOOKAlgebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections.
Nonabelian Algebraic Topology
Author: Ronald Brown
Publisher: JP Medical Ltd
Published: 2011
Total Pages: 714
ISBN-13: 9783037190838
DOWNLOAD EBOOKThe main theme of this book is that the use of filtered spaces rather than just topological spaces allows the development of basic algebraic topology in terms of higher homotopy groupoids; these algebraic structures better reflect the geometry of subdivision and composition than those commonly in use. Exploration of these uses of higher dimensional versions of groupoids has been largely the work of the first two authors since the mid 1960s. The structure of the book is intended to make it useful to a wide class of students and researchers for learning and evaluating these methods, primarily in algebraic topology but also in higher category theory and its applications in analogous areas of mathematics, physics, and computer science. Part I explains the intuitions and theory in dimensions 1 and 2, with many figures and diagrams, and a detailed account of the theory of crossed modules. Part II develops the applications of crossed complexes. The engine driving these applications is the work of Part III on cubical $\omega$-groupoids, their relations to crossed complexes, and their homotopically defined examples for filtered spaces. Part III also includes a chapter suggesting further directions and problems, and three appendices give accounts of some relevant aspects of category theory. Endnotes for each chapter give further history and references.
Rational Homotopy Theory
Author: Yves Felix
Publisher: Springer Science & Business Media
Published: 2001
Total Pages: 589
ISBN-13: 0387950680
DOWNLOAD EBOOKThis is a long awaited book on rational homotopy theory which contains all the main theorems with complete proofs, and more elementary proofs for many results that were proved ten or fifteen years ago. The authors added a frist section on classical algebraic topology to make the book accessible to students with only little background in algebraic topology.
Algebraic Methods in Unstable Homotopy Theory
Author: Joseph Neisendorfer
Publisher: Cambridge University Press
Published: 2010-02-18
Total Pages: 575
ISBN-13: 1139482599
DOWNLOAD EBOOKThe most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which are needed in the presentation of results, proven by Cohen, Moore, and the author, on the exponents of homotopy groups. The author introduces various aspects of unstable homotopy theory, including: homotopy groups with coefficients; localization and completion; the Hopf invariants of Hilton, James, and Toda; Samelson products; homotopy Bockstein spectral sequences; graded Lie algebras; differential homological algebra; and the exponent theorems concerning the homotopy groups of spheres and Moore spaces. This book is suitable for a course in unstable homotopy theory, following a first course in homotopy theory. It is also a valuable reference for both experts and graduate students wishing to enter the field.
Categorical Homotopy Theory
Author: Emily Riehl
Publisher: Cambridge University Press
Published: 2014-05-26
Total Pages: 371
ISBN-13: 1139952633
DOWNLOAD EBOOKThis book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
