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

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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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Authors and Affiliations

  1. Department of Mathematics, U. C. Santa Barbara, Santa Barbara, CA 93106, USA

    Jon McCammond

  2. Department of Mathematics, Lafayette College, Easton, PA 18042, USA

    John Meier

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  1. Jon McCammond
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  2. John Meier
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Correspondence to John Meier.

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Partially supported by NSF grant no. DMS-0101506

Partially supported by an AMS Centennial Research Fellowship

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McCammond, J., Meier, J. The hypertree poset and the ℓ2-Betti numbers of the motion group of the trivial link. Math. Ann. 328, 633–652 (2004). https://doi.org/10.1007/s00208-003-0499-5

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  • DOI: https://doi.org/10.1007/s00208-003-0499-5

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