Categorical Decomposition Techniques in Algebraic Topology
Categorical Decomposition Techniques in Algebraic Topology

Author: Gregory Arone

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 304

ISBN-13: 303487863X

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The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of "topological modular forms".

Categorical Decomposition Techniques in Algebraic Topology
Categorical Decomposition Techniques in Algebraic Topology

Author: Gregory Arone

Publisher: Springer Science & Business Media

Published: 2003-11-27

Total Pages: 322

ISBN-13: 9783764304003

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The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of "topological modular forms".

Handbook of Homotopy Theory
Handbook of Homotopy Theory

Author: Haynes Miller

Publisher: CRC Press

Published: 2020-01-23

Total Pages: 982

ISBN-13: 1351251619

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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.

Deformation Spaces
Deformation Spaces

Author: Hossein Abbaspour

Publisher: Springer Science & Business Media

Published: 2010-04-21

Total Pages: 174

ISBN-13: 3834896802

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The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.

Equivariant Topology and Derived Algebra
Equivariant Topology and Derived Algebra

Author: Scott Balchin

Publisher: Cambridge University Press

Published: 2021-11-18

Total Pages: 357

ISBN-13: 1108931944

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A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.

Surveys in Contemporary Mathematics
Surveys in Contemporary Mathematics

Author: Nicholas Young

Publisher: Cambridge University Press

Published: 2008

Total Pages: 370

ISBN-13: 0521705649

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A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.

Homotopy Theory of Function Spaces and Related Topics
Homotopy Theory of Function Spaces and Related Topics

Author: Yves Félix

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 246

ISBN-13: 0821849298

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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.

Configuration Spaces
Configuration Spaces

Author: Anders Björner

Publisher: Springer

Published: 2013-12-18

Total Pages: 547

ISBN-13: 8876424318

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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.