Iterated spans and classical topological field theories
Algebraic Topology
2018-11-30 v5 Category Theory
Abstract
We construct higher categories of iterated spans, possibly equipped with extra structure in the form of "local systems", and classify their fully dualizable objects. By the Cobordism Hypothesis, these give rise to framed topological quantum field theories, which are the framed versions of the "classical" TQFTs considered in the quantization programme of Freed-Hopkins-Lurie-Teleman. Using this machinery, we also construct an infinity-category of Lagrangian correspondences between symplectic derived algebraic stacks and show that all its objects are fully dualizable.
Cite
@article{arxiv.1409.0837,
title = {Iterated spans and classical topological field theories},
author = {Rune Haugseng},
journal= {arXiv preprint arXiv:1409.0837},
year = {2018}
}
Comments
Accepted version, plus corrections to Remarks 10.5 and 10.7. 64 pages