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New York Journal of Mathematics
Volume 25 (2019), 723-744

  

Andrew A. Cooper, Vin de Silva, and Radmila Sazdanovic

On configuration spaces and simplicial complexes

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Published: September 5, 2019.
Keywords: simplicial complex, homology, chromatic polynomial, categorification.
Subject: 55U10, 05C15, 05C31.

Abstract
The n-point configuration space of a space M is a well-known object in topology, geometry, and combinatorics. We introduce a generalization, the simplicial configuration space MS, which takes as its data a simplicial complex S on n vertices, and explore the properties of its homology, considered as an invariant of S.

As in Eastwood-Huggett's geometric categorification of the chromatic polynomial, our construction gives rise to a polynomial invariant of the simplicial complex S, which generalizes and shares several formal properties with the chromatic polynomial.

Acknowledgements

N/A


Author information

Andrew A. Cooper:
Department of Mathematics
Box 8205, North Carolina State University
Raleigh, NC 27695, USA

andrew.cooper@math.ncsu.edu

Vin de Silva:
Millikan Laboratory
Pomona College
Claremont, CA 91711, USA

vin.desilva@pomona.edu

Radmila Sazdanovic:
Department of Mathematics
Box 8205, North Carolina State University
Raleigh, NC 27695, USA

rsazdanovic@math.ncsu.edu