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Models for configuration space in a simplicial complex

Volume 155 / 2019

John D. Wiltshire-Gordon Colloquium Mathematicum 155 (2019), 127-139 MSC: Primary 55R80; Secondary 55U05. DOI: 10.4064/cm7331-5-2018 Published online: 5 November 2018

Abstract

We produce combinatorial models for configuration space in a simplicial complex, and for configurations near a single point (“local configuration space.”) The model for local configuration space is built out of the poset of poset structures on a finite set. The model for global configuration space relies on a combinatorial model for a simplicial complex with a deleted subcomplex. By way of application, we study the nodal curve $y^2 z = x^3 + x^2 z$, obtaining a presentation for its two-strand braid group, a conjectural presentation for its three-strand braid group, and presentations for its two- and three-strand local braid groups near the singular point.

Authors

  • John D. Wiltshire-GordonUW-Madison Department of Mathematics
    Van Vleck Hall
    480 Lincoln Drive
    Madison, WI 53706, U.S.A.
    e-mail

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