Analytic subdivision invariants
Geometric Topology
2008-07-29 v1
Abstract
This paper introduces an inner product on chain complexes of finite simplicial complexes that is well-adapted to the harmonic study of subdivisions. Its definition utilizes a decomposition of the chain spaces that suggests a sequence of subdivision invariants which we show do not all vanish for non-trivial subdivisions. We exhibit a combinatorial lower bound for these invariants and provide an effective algorithm for their computation. Unfortunately, these invariants cannot distinguish every subdivision nor do they necessarily increase over successive subdivisions.
Cite
@article{arxiv.0807.4235,
title = {Analytic subdivision invariants},
author = {Jer-Chin Chuang},
journal= {arXiv preprint arXiv:0807.4235},
year = {2008}
}