Finite Order q-Invariants of Immersions of Surfaces into 3-Space
Geometric Topology
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/9903161,
title = {Finite Order q-Invariants of Immersions of Surfaces into 3-Space},
author = {Tahl Nowik},
journal= {arXiv preprint arXiv:math/9903161},
year = {2007}
}