Finite-type invariants for curves on surfaces
arXiv:0803.2082
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.
8 pages, The earlier versions contain mistakes at the title and Theorem 5.2 in ver 2 (: Theorem 4.2 in ver 1)