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
Abstract
Let $\operatorname{Aut}(H_1(N_g;\mathbb Z_2),\cdot )$ be the group of automorphisms on the first homology group with $\mathbb Z_2$ coefficient of a closed non-orientable surface $N_g$ preserving the mod $2$ intersection form. In this paper, we obtain a finite presentation for $\operatorname{Aut}(H_1(N_g;\mathbb Z_2),\cdot )$. As applications we calculate the first homology group and the second homology group of $\operatorname{Aut}(H_1(N_g;\mathbb Z_2),\cdot )$.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.7138
- arXiv:
- arXiv:1410.7138
- Bibcode:
- 2014arXiv1410.7138K
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Group Theory
- E-Print:
- 14 pages, 6 figures