Homeomorphisms and the homology of non-orientable surfaces
classification
🧮 math.GN
keywords
non-orientablesurfacesautomorphismclosedcorrespondinghomeomorphismhomeomorphismshomology
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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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