On higher scissors congruence
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909294290534400 |
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| author | Malkiewich, Cary |
| author_facet | Malkiewich, Cary |
| contents | We solve the higher version of Hilbert's Third Problem for one-dimensional geometries, and in higher dimensions we reduce the problem to a computation in group homology. Our central result concerns the scissors congruence $K$-theory spectrum of Zakharevich, whose homotopy groups are the correct higher version of the classical scissors congruence groups. We prove that this spectrum is a Thom spectrum, whose base space is the homotopy orbit space of a Tits complex. The relevant computations quickly follow from this more foundational result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_08082 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On higher scissors congruence Malkiewich, Cary Algebraic Topology K-Theory and Homology 19D99, 55P42, 52B45 We solve the higher version of Hilbert's Third Problem for one-dimensional geometries, and in higher dimensions we reduce the problem to a computation in group homology. Our central result concerns the scissors congruence $K$-theory spectrum of Zakharevich, whose homotopy groups are the correct higher version of the classical scissors congruence groups. We prove that this spectrum is a Thom spectrum, whose base space is the homotopy orbit space of a Tits complex. The relevant computations quickly follow from this more foundational result. |
| title | On higher scissors congruence |
| topic | Algebraic Topology K-Theory and Homology 19D99, 55P42, 52B45 |
| url | https://arxiv.org/abs/2210.08082 |