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2008 Topology of random linkages
Michael Farber
Algebr. Geom. Topol. 8(1): 155-171 (2008). DOI: 10.2140/agt.2008.8.155


Betti numbers of configuration spaces of mechanical linkages (known also as polygon spaces) depend on a large number of parameters – the lengths of the bars of the linkage. Motivated by applications in topological robotics, statistical shape theory and molecular biology, we view these lengths as random variables and study asymptotic values of the average Betti numbers as the number of links n tends to infinity. We establish a surprising fact that for a reasonably ample class of sequences of probability measures the asymptotic values of the average Betti numbers are independent of the choice of the measure. The main results of the paper apply to planar linkages as well as for linkages in 3. We also prove results about higher moments of Betti numbers.


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Michael Farber. "Topology of random linkages." Algebr. Geom. Topol. 8 (1) 155 - 171, 2008.


Received: 21 June 2007; Accepted: 18 December 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1135.55009
MathSciNet: MR2377280
Digital Object Identifier: 10.2140/agt.2008.8.155

Primary: 55N99, 55R80
Secondary: 55M99

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.8 • No. 1 • 2008
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