The $C_2$-equivariant ordinary cohomology of $BU(2)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929586433949696 |
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| author | Costenoble, Steven R. Hudson, Thomas |
| author_facet | Costenoble, Steven R. Hudson, Thomas |
| contents | We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $BU(2)$, the classifying space for $C_2$-equivariant complex 2-plane bundles, using an extended grading that allows us to capture a more natural set of generators. This allows us to define characteristic classes for such bundles. Combined with earlier calculations, it also allows us to define characteristic numbers for equivariant complex lines and surfaces and we give some sample computations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_06411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $C_2$-equivariant ordinary cohomology of $BU(2)$ Costenoble, Steven R. Hudson, Thomas Algebraic Topology Algebraic Geometry 55N91 (Primary) 14M15, 14N15, 55R40, 55R91, 57R20, 57R85 (Secondary) We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $BU(2)$, the classifying space for $C_2$-equivariant complex 2-plane bundles, using an extended grading that allows us to capture a more natural set of generators. This allows us to define characteristic classes for such bundles. Combined with earlier calculations, it also allows us to define characteristic numbers for equivariant complex lines and surfaces and we give some sample computations. |
| title | The $C_2$-equivariant ordinary cohomology of $BU(2)$ |
| topic | Algebraic Topology Algebraic Geometry 55N91 (Primary) 14M15, 14N15, 55R40, 55R91, 57R20, 57R85 (Secondary) |
| url | https://arxiv.org/abs/2411.06411 |