Analytic subdivision invariants

Details Analytic subdivision invariants Analytic subdivision invariants

2008-07-26

arxiv.org/abs/0807.4235v1

Mathematics

Geometric Topology

Scientific paper

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.

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