Bredon sheaf cohomology
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911578409926656 |
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| author | Arnone, Guido Mukherjee, Devarshi Nikolaus, Thomas |
| author_facet | Arnone, Guido Mukherjee, Devarshi Nikolaus, Thomas |
| contents | For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivariant $E$-theory of the $C^*$-algebra of continuous functions. These invariants admit natural descriptions in terms of a new equivariant cohomology theory, which we call Bredon sheaf cohomology.
This theory recovers classical Bredon cohomology for $G$-CW complexes and ordinary sheaf cohomology when $G$ is trivial. We establish its basic structural properties and prove a strong uniqueness theorem: any functor from the category of locally compact Hausdorff $G$-spaces to a dualizable stable category satisfying equivariant open descent and cofiltered compact codescent is equivalent to Bredon sheaf cohomology, generalizing a result of Clausen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08066 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bredon sheaf cohomology Arnone, Guido Mukherjee, Devarshi Nikolaus, Thomas K-Theory and Homology Algebraic Topology Operator Algebras 55N30, 55P91, 18F25 For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivariant $E$-theory of the $C^*$-algebra of continuous functions. These invariants admit natural descriptions in terms of a new equivariant cohomology theory, which we call Bredon sheaf cohomology. This theory recovers classical Bredon cohomology for $G$-CW complexes and ordinary sheaf cohomology when $G$ is trivial. We establish its basic structural properties and prove a strong uniqueness theorem: any functor from the category of locally compact Hausdorff $G$-spaces to a dualizable stable category satisfying equivariant open descent and cofiltered compact codescent is equivalent to Bredon sheaf cohomology, generalizing a result of Clausen. |
| title | Bredon sheaf cohomology |
| topic | K-Theory and Homology Algebraic Topology Operator Algebras 55N30, 55P91, 18F25 |
| url | https://arxiv.org/abs/2604.08066 |