Volume 21, issue 3 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23, 1 issue

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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