Encomplexed Brown Invariant of Real Algebraic Surfaces in RP^3
Geometric Topology
2015-05-30 v1 Algebraic Geometry
Abstract
We construct an invariant of parametrized generic real algebraic surfaces in RP^3 which generalizes the Brown invariant of immersed surfaces from smooth topology. The invariant is constructed using the self intersection, which is a real algebraic curve with points of three local characters: the intersection of two real sheets, the intersection of two complex conjugate sheets or a Whitney umbrella. The Brown invariant was expressed through a self linking number of the self intersection by Kirby and Melvin. We extend the definition of this self linking number to the case of parametrized generic real algebraic surfaces.
Keywords
Cite
@article{arxiv.1108.1566,
title = {Encomplexed Brown Invariant of Real Algebraic Surfaces in RP^3},
author = {Johan Björklund},
journal= {arXiv preprint arXiv:1108.1566},
year = {2015}
}