The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds (K-Monographs in Mathematics)
A.A. Ranicki, A.J. Casson, D.P. Sullivan, M.A. Armstrong, C.P. Rourke, G.E. Cooke
The Hauptvermutung is the conjecture that any two triangulations of a polyhedron are combinatorially equivalent. This 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 further 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. Then, the development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960s. Up to now, the published record of the Hauptvermutung has been incomplete. This volume brings together the original papers of Casson and Sullivan (1967), and the `Princeton Notes on the Hauptvermutung' of Armstrong, Rourke and Cooke (1968/1972). They include several results which have become part of mathematical folklore, but of which proofs had never been published. The material is complemented by an introduction on the Hauptvermutung and an account of recent developments in the area. Also, references have been updated wherever possible. Audience: This book will be valuable to all mathematicians interested in the topology of manifolds, geometry, and differential geometry.
카테고리:
년:
1996
판:
1
출판사:
Springer
언어:
english
페이지:
194
ISBN 10:
0792341740
ISBN 13:
9780792341741
파일:
PDF, 1.13 MB
IPFS:
,
english, 1996
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