Volume 21, issue 3 (2021)

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Configuration spaces of squares in a rectangle

Leonid Plachta

Algebraic & Geometric Topology 21 (2021) 1445–1478
Abstract

The configuration space Fk(Q,r) of k squares of size r in a rectangle Q is studied with the help of the tautological function 𝜃 defined on the affine polytope complex Qk. The critical points of the function 𝜃 are described in geometric and combinatorial terms. We also show that under certain conditions, the space Fk(Q,r) is connected.

Keywords
configuration space of squares, affine polytope complex, affine Morse-Bott function, tautological function, critical point, saturated graph, deformation retraction
Mathematical Subject Classification 2010
Primary: 57Q99, 57R25, 51M20
References
Publication
Received: 9 May 2019
Revised: 28 May 2020
Accepted: 6 July 2020
Published: 11 August 2021
Authors
Leonid Plachta
AGH University of Science and Technology
Kraków
Poland