4-manifolds, surgery on loops and geometric realization of Tietze transformations

2013/03/26 by Politarczyk, Wojciech
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1303.6502

Abstract

In the paper \citewall₁, C.T.C. Wall proved that two smooth closed simply connected 4-manifolds which are homeomorphic are in fact stably diffeomorphic. We prove a similar result which states that two smooth closed 4-manifolds satisfying certain properties are stably diffeomorphic if and only if their signatures agree. The manifolds in question are obtained by surgery on loops. The methods we use are modified surgery of Kreck \citekreck and Kirby calculus.

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