2008/07/26 by Jer-Chin Chuang, Chuang, Jer-Chin
Engineering · #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Manufacturing Process and Optimization
paper · pdf · doi:10.48550/arxiv.0807.4235
openalex publication_date 2008/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.