Scissors congruence K-theory for equivariant manifolds
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918125209911296 |
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| author | Merling, Mona Ng, Ming Semikina, Julia Blanco, Alba Sendón Williams, Lucas |
| author_facet | Merling, Mona Ng, Ming Semikina, Julia Blanco, Alba Sendón Williams, Lucas |
| contents | We introduce a scissors congruence $K$-theory spectrum which lifts the equivariant scissors congruence groups for compact $G$-manifolds with boundary, and we show that on $π_0$ this is the source of a spectrum level lift of the Burnside ring valued equivariant Euler characteristic of a compact $G$-manifold. We also show that the equivariant scissors congruence groups for varying subgroups assemble into a Mackey functor, which is a shadow of a conjectural higher genuine equivariant structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scissors congruence K-theory for equivariant manifolds Merling, Mona Ng, Ming Semikina, Julia Blanco, Alba Sendón Williams, Lucas Algebraic Topology K-Theory and Homology Primary: 19D55, 19D99, 57R91, Secondary: 19D10, 19A49, 55P91, 55S91 We introduce a scissors congruence $K$-theory spectrum which lifts the equivariant scissors congruence groups for compact $G$-manifolds with boundary, and we show that on $π_0$ this is the source of a spectrum level lift of the Burnside ring valued equivariant Euler characteristic of a compact $G$-manifold. We also show that the equivariant scissors congruence groups for varying subgroups assemble into a Mackey functor, which is a shadow of a conjectural higher genuine equivariant structure. |
| title | Scissors congruence K-theory for equivariant manifolds |
| topic | Algebraic Topology K-Theory and Homology Primary: 19D55, 19D99, 57R91, Secondary: 19D10, 19A49, 55P91, 55S91 |
| url | https://arxiv.org/abs/2501.06928 |