The Hauptvermutung Book : A Collection of Papers on the Topology of Manifolds

Category

Algebraic topology

Store

Wordery

Brand

Springer netherlands

The Hauptvermutung Book : A Collection of Papers on the Topology of Manifolds : Springer : 9780792341741 : 0792341740 : 30 Sep 1996 : 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 in

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