Download Applications Of Reidemeister Torsions To 3 Dimensional Topology full books in PDF, epub, and Kindle. Read online free Applications Of Reidemeister Torsions To 3 Dimensional Topology ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
| Author | : VLADIMIR G. KADOKAMI TURAEV (TOURAEV) (TERUHISA. SUZUKI, MASAAKI.) |
| Publisher | : |
| Total Pages | : |
| Release | : 2019 |
| Genre | : |
| ISBN | : 9789813233706 |
| Author | : Vladimir Turaev |
| Publisher | : Birkhäuser |
| Total Pages | : 128 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034883218 |
This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.
| Author | : Kiyoshi Igusa |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 394 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821831704 |
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 | : Vladimir Turaev |
| Publisher | : Birkhäuser |
| Total Pages | : 201 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034879997 |
From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." —Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. ...Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." —Mathematical Reviews
| Author | : Liviu I. Nicolaescu |
| Publisher | : Walter de Gruyter |
| Total Pages | : 263 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 3110173832 |
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 | : Thaddeus M Cowan |
| Publisher | : World Scientific |
| Total Pages | : 492 |
| Release | : 1995-03-06 |
| Genre | : |
| ISBN | : 9814501433 |
This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory.
| Author | : Liviu I. Nicolaescu |
| Publisher | : Walter de Gruyter |
| Total Pages | : 264 |
| Release | : 2008-08-22 |
| Genre | : Mathematics |
| ISBN | : 311019810X |
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 | : Viktor Vasilʹevich Prasolov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821808982 |
This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.
| Author | : Wolfgang Lück |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 604 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662046873 |
In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
| Author | : Jerzy Jezierski |
| Publisher | : |
| Total Pages | : 276 |
| Release | : 1999 |
| Genre | : Fixed point theory |
| ISBN | : |
