Foam cobordism and the Sah-Arnoux-Fathi invariant
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| Format: | Preprint |
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2024
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| _version_ | 1866929270553575424 |
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| author | Im, Mee Seong Khovanov, Mikhail |
| author_facet | Im, Mee Seong Khovanov, Mikhail |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_06030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Foam cobordism and the Sah-Arnoux-Fathi invariant Im, Mee Seong Khovanov, Mikhail Geometric Topology Dynamical Systems K-Theory and Homology 37E05, 37E99, 18M30, 19D99 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. |
| title | Foam cobordism and the Sah-Arnoux-Fathi invariant |
| topic | Geometric Topology Dynamical Systems K-Theory and Homology 37E05, 37E99, 18M30, 19D99 |
| url | https://arxiv.org/abs/2403.06030 |