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A model for random chain complexes

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Abstract

We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over \(\mathbb {F}_q\), conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then investigate the combinatorial and homological properties of this random chain complex.

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Acknowledgements

The first author would like to thank Peter Bubenik for helpful discussions.

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Authors and Affiliations

  1. Iowa State University, Ames, IA, USA

    Michael J. Catanzaro

  2. Southwest Minnesota State University, Marshall, MN, USA

    Matthew J. Zabka

Authors
  1. Michael J. Catanzaro
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  2. Matthew J. Zabka
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Correspondence to Matthew J. Zabka.

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The authors declare that they have no conflict of interest.

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Communicated by Frau Richter.

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Catanzaro, M.J., Zabka, M.J. A model for random chain complexes. Abh. Math. Semin. Univ. Hambg. 91, 335–344 (2021). https://doi.org/10.1007/s12188-021-00248-w

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  • DOI: https://doi.org/10.1007/s12188-021-00248-w

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