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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.02195 |
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| _version_ | 1866909766285000704 |
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| author | Guaschi, John Juan-Pineda, Daniel |
| author_facet | Guaschi, John Juan-Pineda, Daniel |
| contents | We describe the lower algebraic $K$-theory of the integral group ring of both the pure and full braid groups of the real projective plane $\mathbb{R}P^2$ with $3$ strings, as well as that of the integral group ring of the mapping class group of $\mathbb{R}P^2$ with $3$ marked points. In addition, we give a general formula for the algebraic $K$-theory groups of the group ring of the mapping class group of non-orientable surfaces with k marked points, where $k \geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Braid groups of the projective plane, mapping class groups of non-orientable surfaces and algebraic K-theory of their group rings Guaschi, John Juan-Pineda, Daniel Geometric Topology K-Theory and Homology We describe the lower algebraic $K$-theory of the integral group ring of both the pure and full braid groups of the real projective plane $\mathbb{R}P^2$ with $3$ strings, as well as that of the integral group ring of the mapping class group of $\mathbb{R}P^2$ with $3$ marked points. In addition, we give a general formula for the algebraic $K$-theory groups of the group ring of the mapping class group of non-orientable surfaces with k marked points, where $k \geq 3$. |
| title | Braid groups of the projective plane, mapping class groups of non-orientable surfaces and algebraic K-theory of their group rings |
| topic | Geometric Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2509.02195 |