Foam cobordism and the Sah-Arnoux-Fathi invariant
Geometric Topology
2024-03-12 v1 Dynamical Systems
K-Theory and Homology
Abstract
This is the first in a series of papers where scissor congruence and K-theoretical invariants are related to cobordism groups of foams in various dimensions. A model example is provided where the cobordism group of weighted one-foams is identified, via the Sah-Arnoux-Fathi invariant, with the first homology of the group of interval exchange automorphisms and with the Zakharevich first K-group of the corresponding assembler. Several variations on this cobordism group are computed as well.
Keywords
Cite
@article{arxiv.2403.06030,
title = {Foam cobordism and the Sah-Arnoux-Fathi invariant},
author = {Mee Seong Im and Mikhail Khovanov},
journal= {arXiv preprint arXiv:2403.06030},
year = {2024}
}
Comments
38 pages, many figures