Finite Order q-Invariants of Immersions of Surfaces into 3-Space

Details Finite Order q-Invariants of Immersions of Surfaces into 3-Space Finite Order q-Invariants of Immersions of Surfaces into 3-Space

1999-03-28

arxiv.org/abs/math/9903161v1

Mathematics

Geometric Topology

Scientific paper

Given a surface F, we are interested in Z/2 valued invariants of immersions of F into R^3, which are constant on each connected component of the complement of the quadruple point discriminant in Imm(F,R^3). Such invariants will be called ``q-invariants.'' Given a regular homotopy class A in Imm(F,R^3), we denote by V_n(A) the space of all q-invariants on A of order <= n. We show that if F is orientable, then for each regular homotopy class A and each n, dim(V_n(A) / V_{n-1}(A)) <= 1.

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