A model for random chain complexes

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 F q , conditioned on ensuring that the composition of consecutive boundary maps is the zero map. We then...

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Bibliographic Details
Published in:Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2021-10, Vol.91 (2), p.335-344
Main Authors: Catanzaro, Michael J., Zabka, Matthew J.
Format: Article
Language:English
Subjects:
Algebra
Boundary maps
Chains
Combinatorial analysis
Differential Geometry
Fields (mathematics)
Geometry
Homology
Mathematics
Mathematics and Statistics
Number Theory
Topology
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Summary: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 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.
ISSN:0025-5858
1865-8784
DOI:10.1007/s12188-021-00248-w