$RO(C_2\times C_2)$-graded cohomology ring of a point and applications
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911725540868096 |
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| author | Deng, Bill Voineagu, Mircea |
| author_facet | Deng, Bill Voineagu, Mircea |
| contents | We describe the main properties of the $RO(C_2\times Σ_2)$-graded cohomology ring of a point and apply the results to compute the subring of motivic classes given by the Bredon motivic cohomology of real numbers and to compute $RO(C_2\times Σ_2)$-graded cohomology ring of $E_{Σ_2}C_2$.
This generalizes Voevodsky's identification of motivic cohomology of real numbers with the positive cone of $RO(C_2)$ graded cohomology of a point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $RO(C_2\times C_2)$-graded cohomology ring of a point and applications Deng, Bill Voineagu, Mircea Algebraic Topology Algebraic Geometry K-Theory and Homology We describe the main properties of the $RO(C_2\times Σ_2)$-graded cohomology ring of a point and apply the results to compute the subring of motivic classes given by the Bredon motivic cohomology of real numbers and to compute $RO(C_2\times Σ_2)$-graded cohomology ring of $E_{Σ_2}C_2$. This generalizes Voevodsky's identification of motivic cohomology of real numbers with the positive cone of $RO(C_2)$ graded cohomology of a point. |
| title | $RO(C_2\times C_2)$-graded cohomology ring of a point and applications |
| topic | Algebraic Topology Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2502.00956 |