The Hauptvermutung Book - 9789048147359

Name: The Hauptvermutung Book - 9789048147359
Brand: Springer

Springer

The Hauptvermutung BookA Collection of Papers on the Topology of Manifolds\nAuthor(s): A.A. Ranicki, A.A. Ranicki, A.J. Casson, D.P. Sullivan, M.A. Armstrong, C.P. Rourke, G.E. Cooke\nFormat: Paperback\nPublisher: Springer, Netherlands\nImprint: Springer\nISBN-13: 9789048147359, 978-9048147359\nSynopsis\nThe 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 t.