Betti numbers of random manifolds

Michael Farber*, Thomas Kappeler

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study mathematical expectations of Betti numbers of configuration spaces of planar linkages, viewing the lengths of the bars of the linkage as random variables. Our main result gives an explicit asymptotic formulae for these mathematical expectations for two distinct probability measures describing the statistics of the length vectors when the number of links tends to infinity. In the proof we use a combination of geometric and analytic tools. The average Betti numbers are expressed in terms of volumes of intersections of a simplex with certain half-spaces.

Original languageEnglish
Pages (from-to)205-222
Number of pages18
JournalHomology, Homotopy and Applications
Issue number1
StatePublished - 2008
Externally publishedYes


  • Betti number
  • Linkage
  • Polygon space
  • Random linkage


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