Foam cobordism and the Sah-Arnoux-Fathi invariant
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.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Arnold Mathematical Journal
- Publisher
- Association for Mathematical Research
- Volume
- 012
- Issue
- 001
- Pages
- 1–1
- Publication date
- 29 March 2026
- Language
- EN