Purity of quaternionic conjugation spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911667395231744 |
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| author | Ghosh, Surojit Kumar, Ankit Pande, Lakshit |
| author_facet | Ghosh, Surojit Kumar, Ankit Pande, Lakshit |
| contents | Conjugation spaces relate the cohomology of a space and its fixed points via a degree-halving isomorphism and admit a characterization in terms of homological purity. We extend this framework to the Klein four group, where the corresponding structures exhibit a degree-quartering behavior governed by Dickson invariants. Under a mild assumption, we prove that quaternionic conjugation spaces are homologically pure. As an application, we show that such spaces are both $\mathcal{K}_4$-maximal and $\mathcal{K}_4$-Galois maximal, establishing a connection with Smith--Thom type inequalities in real algebraic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09130 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Purity of quaternionic conjugation spaces Ghosh, Surojit Kumar, Ankit Pande, Lakshit Algebraic Topology 55N91 Conjugation spaces relate the cohomology of a space and its fixed points via a degree-halving isomorphism and admit a characterization in terms of homological purity. We extend this framework to the Klein four group, where the corresponding structures exhibit a degree-quartering behavior governed by Dickson invariants. Under a mild assumption, we prove that quaternionic conjugation spaces are homologically pure. As an application, we show that such spaces are both $\mathcal{K}_4$-maximal and $\mathcal{K}_4$-Galois maximal, establishing a connection with Smith--Thom type inequalities in real algebraic geometry. |
| title | Purity of quaternionic conjugation spaces |
| topic | Algebraic Topology 55N91 |
| url | https://arxiv.org/abs/2605.09130 |