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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Craig Jensen, Jon McCammond and John Meier
Journal: Trans. Amer. Math. Soc. 359 (2007), 2577-2595
MSC (2000): Primary 20J06, 57M07
Published electronically: January 4, 2007
MathSciNet review: 2286046
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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.


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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
Email: jon.mccammond@math.ucsb.edu

John Meier
Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
Email: meierj@lafayette.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-07-03967-0
PII: S 0002-9947(07)03967-0
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
Article copyright: © Copyright 2007 American Mathematical Society