Subgroups of the Mapping Class Group and Quadruple Points of Regular Homotopies

dc.creatorNowik, Tahl
dc.date1999-09-03
dc.date.accessioned2026-07-07T05:30:38Z
dc.date.available2026-07-07T05:30:38Z
dc.descriptionLet F be a closed orientable surface. If i,i':F \to R^3 are two regularly homotopic generic immersions, then it has been shown in [N] that all generic regular homotopies between i and i' have the same number mod 2 of quadruple points. We denote this number by Q(i,i') \in Z/2. We show that for any generic immersion i:F\to R^3 and any diffeomorphism h:F\to F such that i and i\circ h are regularly homotopic, Q(i,i\circ h) = (rank(h_*-Id) + (n+1)e(h)) mod 2, where h_* is the map induced by h on H_1(F,Z/2), n is the genus of F and e(h) is 0 or 1 according to whether h is orientation preserving or reversing, respectively.
dc.description24 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/math/9909020
dc.identifierhttp://arxiv.org/abs/math/9909020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79055
dc.subjectGeometric Topology
dc.titleSubgroups of the Mapping Class Group and Quadruple Points of Regular Homotopies
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