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C*-algebras and Elliptic Theory II (Repost)

Posted By: AvaxGenius
Date: 28 Jan 2024 03:38:48
C*-algebras and Elliptic Theory II (Repost)

C*-algebras and Elliptic Theory II by Dan Burghelea, Richard Melrose, Alexander S. Mishchenko, Evgenij V. Troitsky
English | PDF (True) | 2008 | 312 Pages | ISBN : 3764386037 | 2.7 MB

This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.
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Homotopy Theory of C*-Algebras

Posted By: AvaxGenius
Date: 21 Oct 2022 09:18:56
Homotopy Theory of C*-Algebras

Homotopy Theory of C*-Algebras by Paul Arne Østvær
English | PDF(True) | 2010 | 142 Pages | ISBN : 3034605641 | 1.83 MB

Homotopy theory and C*-algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopy theory and applications.
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Cyclic Homology in Non-Commutative Geometry

Posted By: AvaxGenius
Date: 19 Sep 2022 04:22:00
Cyclic Homology in Non-Commutative Geometry

Cyclic Homology in Non-Commutative Geometry by Joachim Cuntz, Georges Skandalis, Boris Tsygan
English | PDF | 2004 | 147 Pages | ISBN : 3540404694 | 12.2 MB

Cyclic homology was introduced in the early eighties independently by Connes and Tsygan. They came from different directions. Connes wanted to associate homological invariants to K-homology classes and to describe the index pair­ ing with K-theory in that way, while Tsygan was motivated by algebraic K-theory and Lie algebra cohomology. At the same time Karoubi had done work on characteristic classes that led him to study related structures, without however arriving at cyclic homology properly speaking. Many of the principal properties of cyclic homology were already developed in the fundamental article of Connes and in the long paper by Feigin-Tsygan.
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Topology I: General Survey

Posted By: AvaxGenius
Date: 19 Sep 2022 03:57:25
Topology I: General Survey

Topology I: General Survey by S. P. Novikov
English | PDF | 1996 | 326 Pages | ISBN : 3540170073 | 27.5 MB

This book constitutes nothing less than an up-to-date survey of the whole field of topology (with the exception of "general (set-theoretic) topology"), or, in the words of Novikov himself, of what was termed at the end of the 19th century "Analysis Situs", and subsequently diversified into the various subfields of combinatorial, algebraic, differential, homotopic, and geometric topology. The book gives an overview of these subfields, beginning with the elements and proceeding right up to the present frontiers of research.
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Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes (Repost)

Posted By: AvaxGenius
Date: 19 Aug 2022 04:51:25
Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes (Repost)

Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes by Piotr Pragacz
English | PDF | 2005 | 321 Pages | ISBN : 3764372141 | 3 MB

The articles in this volume study various cohomological aspects of algebraic varieties:
- characteristic classes of singular varieties;
- geometry of flag varieties;
- cohomological computations for homogeneous spaces;
- K-theory of algebraic varieties;
- quantum cohomology and Gromov-Witten theory.
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Homotopy Theory with Bornological Coarse Spaces

Posted By: AvaxGenius
Date: 3 Sep 2020 16:59:39
Homotopy Theory with Bornological Coarse Spaces

Homotopy Theory with Bornological Coarse Spaces by Ulrich Bunke
English | PDF,EPUB | 2020 | 248 Pages | ISBN : 3030513343 | 16 MB

Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories. It introduces the category of bornological coarse spaces and the notion of a coarse homology theory, and further constructs the universal coarse homology theory.
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