Work

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

Year: 2026

Type: article

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 $$\mathbb {R}P^2$$ R P 2 with 3 strings, as well as that of the integral group ring of the mapping class group of $$\mathbb {R}P^2$$ 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 $$k\ge 3$$ k ≥ 3 .

Source: Boletín de la Sociedad Matemática Mexicana

DOI: 10.1007/s40590-026-00889-y

Authors: John Guaschi, Daniel Juan-Pineda