Homeomorphisms and the Homology of Non-Orientable Surfaces

[摘要] We show that, for a closed non-orientable surface 𝐹, an automorphism of $H_1(F,mathbb{Z})$ is induced by a homeomorphism of 𝐹 if and only if it preserves the $(mathrm{mod} 2)$ intersection pairing. We shall also prove the corresponding result for punctured surfaces.

[学科分类] 数学（综合）

[关键词] Non-orientable surfaces;Dehn twist;mapping class groups;crosscap slide.