Two-Dimensional Extended Homotopy Field Theories

Kursat Sozer

doi:10.2140/agt.2023.23.3909

Two-Dimensional Extended Homotopy Field Theories

Geometric Topology 2023-11-29 v2 Algebraic Topology

Authors: Kursat Sozer

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We give another definition of two-dimensional extended homotopy field theories (E-HFTs) with aspherical targets and classify them. When the target of E-HFT is chosen to be a $K(G,1)$ -space, we classify E-HFTs taking values in the symmetric monoidal bicategory of algebras, bimodules, and bimodule maps by certain Frobenius $G$ -algebras called quasi-biangular $G$ -algebras. As an application, for any discrete group $G$ , we verify a special case of the $(G \times SO(2))$ -structured cobordism hypothesis due to Lurie.

Keywords

homotopy theory algebraic topology spectral sequences

Cite

@article{arxiv.1909.04187,
  title  = {Two-Dimensional Extended Homotopy Field Theories},
  author = {Kursat Sozer},
  journal= {arXiv preprint arXiv:1909.04187},
  year   = {2023}
}

Comments

Version 2 with 61 pages and 36 figures; the organization of the sections is changed and the arguments are improved in light of the referee's comments and suggestions. To appear in Algebraic & Geometry Topology

Two-Dimensional Extended Homotopy Field Theories

Abstract

Keywords

Cite

Comments

Related papers