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- W2949875198 abstract "Let F be a closed non-orientable surface. We classify all finite order invariants of immersions of F into R^3, with values in any Abelian group. We show they are all functions of the universal order 1 invariant that we construct as T oplus P oplus 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 i,j:Fto R^3, P(i)-P(j) in Z/2 (respectively Q(i)-Q(j) in 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 i:Fto R^3 and diffeomorphism h:Fto F such that i and i circ h are regularly homotopic we show: P(icirc h)-P(i) = Q(icirc h)-Q(i) = (rank(h_* - Id) + E(det h_**)) mod 2 where h_* is the map induced by h on H_1(F;Z/2), h_** is the map induced by h on H_1(F;Q) (Q=the rationals), and for 0 neq q in Q, E(q) in Z/2 is 0 or 1 according to whether q is positive or negative, respectively." @default.
- W2949875198 created "2019-06-27" @default.
- W2949875198 creator A5031950115 @default.
- W2949875198 date "2003-10-02" @default.
- W2949875198 modified "2023-09-27" @default.
- W2949875198 title "Immersions of Non-orientable Surfaces" @default.
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