## The Euler characteristic of the Whitehead automorphism group of a free product

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- by Craig Jensen, Jon McCammond and John Meier PDF
- Trans. Amer. Math. Soc.
**359**(2007), 2577-2595 Request permission

## Abstract:

A combinatorial summation identity over the lattice of labelled hypertrees is established that allows one to gain concrete information on the Euler characteristics of various automorphism groups of free products of groups. In particular, we establish formulae for the Euler characteristics of: the group of Whitehead automorphisms $\mathrm {Wh}(\ast _{i=1}^n G_i)$ when the $G_i$ are of finite homological type; $\operatorname {Aut}(\ast _{i=1}^n G_i)$ and $\operatorname {Out} (\ast _{i=1}^n G_i)$ when the $G_i$ are finite; and the palindromic automorphism groups of finite rank free groups.## References

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## Additional Information

**Craig Jensen**- Affiliation: Department of Mathematics, University of New Orleans, New Orleans, Louisiana 70148
- Email: jensen@math.uno.edu
**Jon McCammond**- Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
- MR Author ID: 311045
- Email: jon.mccammond@math.ucsb.edu
**John Meier**- Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
- Email: meierj@lafayette.edu
- Received by editor(s): September 15, 2004
- Received by editor(s) in revised form: February 9, 2005
- Published electronically: January 4, 2007
- Additional Notes: The first author was partially supported by Louisiana Board of Regents RCS contract no. LEQSF-RD-A-39

The second author was partially supported by NSF grant no. DMS-0101506

The third author was partially supported by an AMS Centennial Research Fellowship - © Copyright 2007 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**359**(2007), 2577-2595 - MSC (2000): Primary 20J06, 57M07
- DOI: https://doi.org/10.1090/S0002-9947-07-03967-0
- MathSciNet review: 2286046