Finite Order q-Invariants of Immersions of Surfaces into 3-Space
Abstract
Given a surface F, we are interested in Z/2 valued invariants of immersions of F into R3, which are constant on each connected component of the complement of the quadruple point discriminant in Imm(F,R3). Such invariants will be called ``q-invariants.'' Given a regular homotopy class A in Imm(F,R3), we denote by Vn(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(Vn(A) / Vn-1(A)) <= 1.
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