Configuration spaces of squares in a rectangle
type: Item
instance of: scholarly article
title: Configuration spaces of squares in a rectangle
zbMATH Open document ID: 1483.57031
author: Leonid Plachta
published in: Algebraic \& Geometric Topology
publication date: 2021-09-10T00:00:00Z
review text: The author studies the configuration space \(F_k(Q;r)\) of \(k\) squares of size \(r\) in a rectangle \(Q\), by using the tautological function \(\theta\) defined on the affine polytope complex \(Q^k\). The critical points of the function \(\theta\) are described in geometric and combinatorial terms. It is also proved that under certain conditions, the space \(F_k(Q;r)\) is connected. The paper is organized into three sections dealing with the following aspects: Introduction, affine Morse-Bott functions on affine polytope complexes, configuration spaces of squares in a rectangle (first surgery of \(F_k(Q;r)\), connectivity of \(F_n(Q;r)\)).
reviewed by: Dorin Andrica
Mathematics Subject Classification ID: 57Q99
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 55R80
zbMATH DE Number: 7394052
zbMATH Keywords: configuration space of squares
zbMATH Keywords: affine polytope complex
zbMATH Keywords: affine Morse-Bott function
zbMATH Keywords: tautological function
zbMATH Keywords: critical point
zbMATH Keywords: saturated graph
zbMATH Keywords: deformation retraction
MaRDI profile type: Publication
full work available at URL: agt.2021.21.1445
OpenAlex ID: W3195704816
cites work: Discrete configuration spaces of squares and hexagons
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DOI: 10.2140/AGT.2021.21.1445
description: scientific article; zbMATH DE number 7394052