Finite-type invariants for curves on surfaces
Geometric Topology
2008-10-15 v3
Abstract
This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a higher-order generalisation of a part of Arnold's invariants that are first-order invariants for plane immersed curves. The invariants in this theory are developed using the word theory proposed by Turaev.
Cite
@article{arxiv.0803.2082,
title = {Finite-type invariants for curves on surfaces},
author = {Noboru Ito},
journal= {arXiv preprint arXiv:0803.2082},
year = {2008}
}
Comments
8 pages, The earlier versions contain mistakes at the title and Theorem 5.2 in ver 2 (: Theorem 4.2 in ver 1)