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A Homology Theory for Smale Spaces

2014-09-29 Mathematics
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Release : 2014-09-29
Genre : Mathematics
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Book Rating : 097/5 ( reviews)

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Book Synopsis A Homology Theory for Smale Spaces by : Ian F. Putnam

Download or read book A Homology Theory for Smale Spaces written by Ian F. Putnam. This book was released on 2014-09-29. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a homology theory for Smale spaces, which include the basics sets for an Axiom A diffeomorphism. It is based on two ingredients. The first is an improved version of Bowen's result that every such system is the image of a shift of finite type under a finite-to-one factor map. The second is Krieger's dimension group invariant for shifts of finite type. He proves a Lefschetz formula which relates the number of periodic points of the system for a given period to trace data from the action of the dynamics on the homology groups. The existence of such a theory was proposed by Bowen in the 1970s.

Homology and K-theory of Torsion-free Ample Groupoids and Smale Spaces

2020
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Release : 2020
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Book Synopsis Homology and K-theory of Torsion-free Ample Groupoids and Smale Spaces by : Valerio Proietti

Download or read book Homology and K-theory of Torsion-free Ample Groupoids and Smale Spaces written by Valerio Proietti. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt:

Homotopy Theory with Bornological Coarse Spaces

2020-09-03 Mathematics
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Release : 2020-09-03
Genre : Mathematics
Kind : eBook
Book Rating : 351/5 ( reviews)

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Book Synopsis Homotopy Theory with Bornological Coarse Spaces by : Ulrich Bunke

Download or read book Homotopy Theory with Bornological Coarse Spaces written by Ulrich Bunke. This book was released on 2020-09-03. Available in PDF, EPUB and Kindle. Book excerpt: 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. Hybrid structures are introduced as a tool to connect large-scale with small-scale geometry, and are then employed to describe the coarse motives of bornological coarse spaces of finite asymptotic dimension. The remainder of the book is devoted to the construction of examples of coarse homology theories, including an account of the coarsification of locally finite homology theories and of coarse K-theory. Thereby it develops background material about locally finite homology theories and C*-categories. The book is intended for advanced graduate students and researchers who want to learn about the homotopy-theoretical aspects of large scale geometry via the theory of infinity categories.

An Introduction to Intersection Homology Theory

1988 Algebra, Homological
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Release : 1988
Genre : Algebra, Homological
Kind : eBook
Book Rating : 984/5 ( reviews)

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Book Synopsis An Introduction to Intersection Homology Theory by : Frances Clare Kirwan

Download or read book An Introduction to Intersection Homology Theory written by Frances Clare Kirwan. This book was released on 1988. Available in PDF, EPUB and Kindle. Book excerpt:

Operator Algebras and Applications

2016-07-30 Mathematics
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Release : 2016-07-30
Genre : Mathematics
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Book Rating : 867/5 ( reviews)

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Book Synopsis Operator Algebras and Applications by : Toke M. Carlsen

Download or read book Operator Algebras and Applications written by Toke M. Carlsen. This book was released on 2016-07-30. Available in PDF, EPUB and Kindle. Book excerpt: Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject. The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis. This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.

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