Mathematische Annalen

, Volume 328, Issue 4, pp 633–652 | Cite as

The hypertree poset and the ℓ2-Betti numbers of the motion group of the trivial link

Article

Abstract

We give explicit formulae for the Euler characteristic and ℓ2-cohomology of the group of motions of the trivial link, or isomorphically the group of free group automorphisms that send each standard generator to a conjugate of itself. The method is primarily combinatorial and ultimately relies on a computation of the Möbius function for the poset of labelled hypertrees.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsUSA
  2. 2.Department of MathematicsUSA

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