A finite presentation for the automorphism group of the first homology of a non-orientable surface over $\mathbb Z_2$ preserving the mod $2$ intersection form

Ryoma Kobayashi; Genki Omori

paper

A finite presentation for the automorphism group of the first homology of a non-orientable surface over $Z_{2}$ preserving the mod $2$ intersection form

arXiv:1410.7138

Abstract

Let $Aut (H_{1} (N_{g}; Z_{2}), \cdot)$ be the group of automorphisms on the first homology group with $Z_{2}$ coefficient of a closed non-orientable surface $N_{g}$ preserving the mod $2$ intersection form. In this paper, we obtain a finite presentation for $Aut (H_{1} (N_{g}; Z_{2}), \cdot)$ . As applications we calculate the first homology group and the second homology group of $Aut (H_{1} (N_{g}; Z_{2}), \cdot)$ .

14 pages, 6 figures

A finite presentation for the automorphism group of the first homology of a non-orientable surface over Z2​ preserving the mod 2 intersection form

Abstract

A finite presentation for the automorphism group of the first homology of a non-orientable surface over $Z_{2}$ preserving the mod $2$ intersection form