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Author : David Ambrose
Release : 1964
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Reidemeister Torsion in Finite Simplicial Complexes by : David Ambrose
Download or read book Reidemeister Torsion in Finite Simplicial Complexes written by David Ambrose. This book was released on 1964. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kiyoshi Igusa
Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 704/5 ( reviews)
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.
Author : Liviu I. Nicolaescu
Release : 2008-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 10X/5 ( reviews)
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.
Author : Liviu I. Nicolaescu
Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 832/5 ( reviews)
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 2003. Available in PDF, EPUB and Kindle. Book excerpt: This work discusses the theoretical foundations of torsion, one of the oldest topological variants. It presents the work of Reidmeister, Taubes, Turaev and the author, focusing particularly on diverse examples and techniques rather than abstract generalizations.
Author : Pierre Albin
Release : 2021-06-21
Genre : Education
Kind : eBook
Book Rating : 224/5 ( reviews)
Book Synopsis Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps by : Pierre Albin
Download or read book Resolvent, Heat Kernel, and Torsion under Degeneration to Fibered Cusps written by Pierre Albin. This book was released on 2021-06-21. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds with fibered cusps are a class of complete non-compact Riemannian manifolds including many examples of locally symmetric spaces of rank one. We study the spectrum of the Hodge Laplacian with coefficients in a flat bundle on a closed manifold undergoing degeneration to a manifold with fibered cusps. We obtain precise asymptotics for the resolvent, the heat kernel, and the determinant of the Laplacian. Using these asymptotics we obtain a topological description of the analytic torsion on a manifold with fibered cusps in terms of the R-torsion of the underlying manifold with boundary.
