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Author | : A.A. Ranicki |
Publisher | : Springer Science & Business Media |
Total Pages | : 192 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401733430 |
Download The Hauptvermutung Book Book in PDF, ePub and Kindle
The Hauptvermutung is the conjecture that any two triangulations of a poly hedron are combinatorially equivalent. The conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that furt her development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. These polyhedra were not manifolds, leaving open the Hauptvermu tung for manifolds. The development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960's. Unfortunately, the published record of the manifold Hauptvermutung has been incomplete, as was forcefully pointed out by Novikov in his lecture at the Browder 60th birthday conference held at Princeton in March 1994. This volume brings together the original 1967 papers of Casson and Sulli van, and the 1968/1972 'Princeton notes on the Hauptvermutung' of Armstrong, Rourke and Cooke, making this work physically accessible. These papers include several other results which have become part of the folklore but of which proofs have never been published. My own contribution is intended to serve as an intro duction to the Hauptvermutung, and also to give an account of some more recent developments in the area. In preparing the original papers for publication, only minimal changes of punctuation etc.
Author | : Robin C. Kirby |
Publisher | : |
Total Pages | : 16 |
Release | : 1969 |
Genre | : |
ISBN | : |
Download On the Triangulation of Manifolds and the Hauptvermutung Book in PDF, ePub and Kindle
Author | : Edward Martin Brown |
Publisher | : |
Total Pages | : 256 |
Release | : 1963 |
Genre | : |
ISBN | : |
Download The Hauptvermutung for 3-complexes Book in PDF, ePub and Kindle
Author | : Robion C. Kirby |
Publisher | : Princeton University Press |
Total Pages | : 376 |
Release | : 1977-05-21 |
Genre | : Mathematics |
ISBN | : 9780691081915 |
Download Foundational Essays on Topological Manifolds, Smoothings, and Triangulations Book in PDF, ePub and Kindle
Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Author | : Mathematisches Forschungsinstitut Oberwolfach |
Publisher | : |
Total Pages | : 31 |
Release | : 2006 |
Genre | : |
ISBN | : |
Download The Hauptvermutung for High Dimensional Manifolds Book in PDF, ePub and Kindle
Author | : Dimitry Kozlov |
Publisher | : Springer Science & Business Media |
Total Pages | : 416 |
Release | : 2008-01-08 |
Genre | : Mathematics |
ISBN | : 9783540730514 |
Download Combinatorial Algebraic Topology Book in PDF, ePub and Kindle
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
Author | : Colin Patrick Rourke |
Publisher | : |
Total Pages | : 42 |
Release | : 1968 |
Genre | : Homotopy theory |
ISBN | : |
Download The Hauptvermutung According to Sullivan Book in PDF, ePub and Kindle
Author | : Michael Henle |
Publisher | : Courier Corporation |
Total Pages | : 340 |
Release | : 1994-01-01 |
Genre | : Mathematics |
ISBN | : 9780486679662 |
Download A Combinatorial Introduction to Topology Book in PDF, ePub and Kindle
Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
Author | : Mark Anthony Armstrong |
Publisher | : |
Total Pages | : |
Release | : 1967 |
Genre | : |
ISBN | : |
Download Lectures on the hauptvermutung according to Lashof and Rothenberg Book in PDF, ePub and Kindle
Author | : Charles Terence Clegg Wall |
Publisher | : American Mathematical Soc. |
Total Pages | : 321 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821809423 |
Download Surgery on Compact Manifolds Book in PDF, ePub and Kindle
The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.