Braid groups of the projective plane, mapping class groups of non-orientable surfaces and algebraic K-theory of their group rings

John Guaschi; Daniel Juan-Pineda

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arXiv · 2509.02195

Braid groups of the projective plane, mapping class groups of non-orientable surfaces and algebraic K-theory of their group rings

John Guaschi·Daniel Juan-Pineda

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Abstract

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 $k \geq 3$.

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BibTeX RIS

John Guaschi, Daniel Juan-Pineda. 2025-09-02. Braid groups of the projective plane, mapping class groups of non-orientable surfaces and algebraic K-theory of their group rings. https://arxiv.org/abs/2509.02195

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