4-manifolds, surgery on loops and geometric realization of Tietze transformations
Geometric Topology
2013-04-02 v3 Algebraic Topology
Abstract
In the paper \cite{wall_1}, 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 \cite{kreck} and Kirby calculus.
Keywords
Cite
@article{arxiv.1303.6502,
title = {4-manifolds, surgery on loops and geometric realization of Tietze transformations},
author = {Wojciech Politarczyk},
journal= {arXiv preprint arXiv:1303.6502},
year = {2013}
}