Mathematische Annalen

, Volume 328, Issue 4, pp 633–652

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


DOI: 10.1007/s00208-003-0499-5

Cite this article as:
McCammond, J. & Meier, J. Math. Ann. (2004) 328: 633. doi:10.1007/s00208-003-0499-5


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

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