Combinatorial equivalence of real moduli spaces
Satyan L. Devadoss
TL;DR
This paper presents a novel combinatorial construction of the real moduli space of spheres by relating associahedra, obtained from truncations of products of simplices, to blow-ups of the braid hyperplane arrangement.
Contribution
It introduces a new way to realize associahedra as truncations of products of simplices, connecting them to the real moduli space of spheres and hyperplane arrangements.
Findings
Associations are realized as truncations of products of simplices.
The construction relates the moduli space to blow-ups of the braid arrangement.
Provides a combinatorial perspective on real moduli spaces.
Abstract
A well-known construction of associahedra comes from truncations of simplices. Motivated by compactifications of point configurations, we show associahedra as truncations of certain products of simplices. This is then used to provide a combinatorial construction of the real moduli space of spheres relating it to blow-ups of the braid hyperplane arrangement.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Computability, Logic, AI Algorithms