Homeomorphisms and the Homology of Non-Orientable Surfaces

Proceedings Mathematical Sciences

Siddhartha Gadgil²  Dishant Pancholi¹ 

[1] School of Mathematics, Tata Institute of Fundamental Research, Mumbai 00 00, India$$;Stat Math Unit, Indian Statistical Institute, Bangalore 0 0, India$$

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

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 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.

【 授权许可】

Unknown