Configuration Spaces of Points: A User's Guide

2024/07/14 by Sadok Kallel, Kallel, Sadok · 1 voice · 3 citations
Mathematics · #math-ph #math.AT

paper · pdf · doi:10.48550/arxiv.2407.11092

Abstract

This user's guide (updated version) consists of two parts. The first part is an extensive survey contributed to the Encyclopedia of Mathematical Physics, 2nd edition. It covers many of the main constructions, definitions, and applications of the classical configuration spaces of points. The second part delves into the geometry of chromatic configuration spaces, giving a detailed proof of the remarkable result that the Poincaré polynomial of the chromatic configuration spaces of \mathbb R^N, associated to a finite simple graph Γ, corresponds to the reciprocal of the chromatic polynomial of the graph (with signs). Further applications and a stable splitting are given.

Cited by

• The asphericity of locally finite infinite configuration spaces and Weierstrass entire coverings
• Renormalization of Chern-Simons Wilson Loops via Flux Quantization in Cohomotopy
• Graphical configuration spaces, Contractads and Formality

Discussions

• If you know some algebraic topology, this looks like a great introduction to configuration spaces: arxiv.org/abs/2407.11092 🧮 [bsky, 7 points, 2 comments]

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