Foam cobordism and the Sah-Arnoux-Fathi invariant

Mee Seong Im; Mikhail Khovanov

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arXiv · 2403.06030

Foam cobordism and the Sah-Arnoux-Fathi invariant

Mee Seong Im·Mikhail Khovanov

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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.

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Mee Seong Im, Mikhail Khovanov. 2024-03-09. Foam cobordism and the Sah-Arnoux-Fathi invariant. https://arxiv.org/abs/2403.06030

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