Geodesic
Configuration spaces of thick particles on a metric graph
Deeley, Kenneth1
1Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK
Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 1861-1892
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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)).

DOI : 10.2140/agt.2011.11.1861
Classification : 55R80, 57Q05, 57M15
Keywords: topology of configuration spaces, metric graph, PL topology, topological robotics

Deeley, Kenneth  1

1 Department of Mathematical Sciences, Durham University, Durham DH1 3LE, UK 
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Deeley, Kenneth. Configuration spaces of thick particles on a metric graph. Algebraic and Geometric Topology, Tome 11 (2011) no. 4, pp. 1861-1892. doi: 10.2140/agt.2011.11.1861

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