Immersions of non-orientable surfaces |
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Authors: | Tahl Nowik |
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Institution: | Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel |
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Abstract: | Let F be a closed non-orientable surface. We classify all finite order invariants of immersions of F into R3, with values in any Abelian group. We show they are all functions of a universal order 1 invariant which we construct as T⊕P⊕Q, where T is a Z valued invariant reflecting the number of triple points of the immersion, and P,Q are Z/2 valued invariants characterized by the property that for any regularly homotopic immersions , P(i)−P(j)∈Z/2 (respectively, Q(i)−Q(j)∈Z/2) is the number mod 2 of tangency points (respectively, quadruple points) occurring in any generic regular homotopy between i and j.For immersion and diffeomorphism such that i and i○h are regularly homotopic we show: P(i○h)−P(i)=Q(i○h)−Q(i)=(rank(h∗−Id)+ε(deth∗∗))mod2 |
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Keywords: | Immersions of surfaces Finite order invariants |
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