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Higher Franz-Reidemeister Torsion

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 704/5 ( reviews)

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Book Synopsis Higher Franz-Reidemeister Torsion by : Kiyoshi Igusa

Download or read book Higher Franz-Reidemeister Torsion written by Kiyoshi Igusa. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: This work is devoted to the theory of topological higher Franz-Reidemeister torsion in $K$-theory. The author defines the higher Franz-Reidemeister torsion based on Volodin's $K$-theory and Borel's regulator map. He describes its properties and generalizations and studies the relation between the higher Franz-Reidemeister torsion and other torsions used in $K$-theory: Whitehead torsion and Ray-Singer torsion. He also presents methods of computing higher Franz-Reidemeister torsion, illustrates them with numerous examples, and describes various applications of higher Franz-Reidemeister torsion, particularly for the study of homology of mapping class groups. Packed with up-to-date information, the book should provide a useful research and reference tool for specialists working in algebraic topology and $K$-theory.

Higher Complex Torsion and the Framing Principle

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 737/5 ( reviews)

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Book Synopsis Higher Complex Torsion and the Framing Principle by : Kiyoshi Igusa

Download or read book Higher Complex Torsion and the Framing Principle written by Kiyoshi Igusa. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: Intends to prove that higher Franz-Reidemeister (FR) torsion satisfies the transfer property and a formula known as the 'Framing Principle' in full generality. This title uses these properties to compute the higher FR-torsion for various smooth bundles with oriented closed even dimensional manifold fibers.

The Reidemeister Torsion of 3-Manifolds

2008-08-22 Mathematics
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Release : 2008-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 10X/5 ( reviews)

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Book Synopsis The Reidemeister Torsion of 3-Manifolds by : Liviu I. Nicolaescu

Download or read book The Reidemeister Torsion of 3-Manifolds written by Liviu I. Nicolaescu. This book was released on 2008-08-22. Available in PDF, EPUB and Kindle. Book excerpt: This is a state-of-the-art introduction to the work of Franz Reidemeister, Meng Taubes, Turaev, and the author on the concept of torsion and its generalizations. Torsion is the oldest topological (but not with respect to homotopy) invariant that in its almost eight decades of existence has been at the center of many important and surprising discoveries. During the past decade, in the work of Vladimir Turaev, new points of view have emerged, which turned out to be the "right ones" as far as gauge theory is concerned. The book features mostly the new aspects of this venerable concept. The theoretical foundations of this subject are presented in a style accessible to those, who wish to learn and understand the main ideas of the theory. Particular emphasis is upon the many and rather diverse concrete examples and techniques which capture the subleties of the theory better than any abstract general result. Many of these examples and techniques never appeared in print before, and their choice is often justified by ongoing current research on the topology of surface singularities. The text is addressed to mathematicians with geometric interests who want to become comfortable users of this versatile invariant.

Mapping Class Groups and Moduli Spaces of Riemann Surfaces

1993 Mathematics
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Release : 1993
Genre : Mathematics
Kind : eBook
Book Rating : 675/5 ( reviews)

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Book Synopsis Mapping Class Groups and Moduli Spaces of Riemann Surfaces by : Carl-Friedrich Bödigheimer

Download or read book Mapping Class Groups and Moduli Spaces of Riemann Surfaces written by Carl-Friedrich Bödigheimer. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt: The study of mapping class groups and moduli spaces of compact Riemann surfaces is currently a central topic in topology, algebraic geometry, and conformal field theory. This book contains proceedings from two workshops held in the summer of 1991, one at the University of G\"ottingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, the book appeals to mathematicians and physicists.

Regulators in Analysis, Geometry and Number Theory

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 153/5 ( reviews)

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Book Synopsis Regulators in Analysis, Geometry and Number Theory by : Alexander Reznikov

Download or read book Regulators in Analysis, Geometry and Number Theory written by Alexander Reznikov. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: "This work is an outgrowth of a conference held at the Hebrew University in Jerusalem on Regulators in Analysis, Geometry and Number Theory, and should appeal to a broad audience of graduate students and research mathematicians."--BOOK JACKET.

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