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Homeomorphisms and the homology of non-orientable surfaces

Siddhartha Gadgil·Dishant Pancholi
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Abstract

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

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Siddhartha Gadgil, Dishant Pancholi. 2006-07-27. Homeomorphisms and the homology of non-orientable surfaces. https://arxiv.org/abs/math/0607693

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