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2011 Configuration spaces of thick particles on a metric graph
Kenneth Deeley
Algebr. Geom. Topol. 11(4): 1861-1892 (2011). DOI: 10.2140/agt.2011.11.1861

Abstract

We study the topology of configuration spaces Fr(Γ,2) of two thick particles (robots) of radius r>0 moving on a metric graph Γ. As the size of the robots increases, the topology of Fr(Γ,2) varies. Given Γ and r, we provide an algorithm for computing the number of path components of Fr(Γ,2). Using our main tool of PL Morse–Bott theory, we show that there are finitely many critical values of r where the homotopy type of Fr(Γ,2) changes. We study the transition across a critical value R(a,b) by computing the ranks of the relative homology groups of (Fa(Γ,2),Fb(Γ,2)).

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Kenneth Deeley. "Configuration spaces of thick particles on a metric graph." Algebr. Geom. Topol. 11 (4) 1861 - 1892, 2011. https://doi.org/10.2140/agt.2011.11.1861

Information

Received: 23 October 2010; Revised: 15 March 2011; Accepted: 26 April 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1230.55010
MathSciNet: MR2826926
Digital Object Identifier: 10.2140/agt.2011.11.1861

Subjects:
Primary: 55R80, 57Q05
Secondary: 57M15

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2011
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