Vanishing homology
Algebraic Geometry
2008-01-15 v1
Abstract
In this paper we introduce a new homology theory devoted to the study of families such as semi-algebraic or subanalytic families and in general to any family definable in an o-minimal structure (such as Denjoy-Carleman definable or definable sets). The idea is to study the cycles which are vanishing when we approach a special fiber. This also enables us to derive local metric invariants for germs of definable sets. We prove that the homology groups are finitely generated.
Cite
@article{arxiv.0801.2109,
title = {Vanishing homology},
author = {Guillaume Valette},
journal= {arXiv preprint arXiv:0801.2109},
year = {2008}
}