High-Dimensional Topological Field Theory, Positivity, and Exotic Smooth Spheres
Algebraic Topology
2015-08-07 v1 Mathematical Physics
math.MP
Abstract
In previous work, we proposed a general framework of positive topological field theories (TFTs) based on Eilenberg's notion of summation completeness for semirings. In the present paper, we apply this framework in constructing explicitly a concrete positive TFT defined on smooth manifolds of any dimension greater than 1. We prove that this positive TFT detects exotic smooth spheres. We show further that polynomial invariants (subject to boundary conditions) can be extracted from the state sum if the dimension of the cobordisms is at least 3.
Keywords
Cite
@article{arxiv.1508.01337,
title = {High-Dimensional Topological Field Theory, Positivity, and Exotic Smooth Spheres},
author = {Markus Banagl},
journal= {arXiv preprint arXiv:1508.01337},
year = {2015}
}