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Graev metrics on free products and HNN extensions

Author: Konstantin Slutsky
Journal: Trans. Amer. Math. Soc. 366 (2014), 6353-6395
MSC (2010): Primary 54H11, 03E15
Published electronically: June 25, 2014
MathSciNet review: 3267013
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Abstract: We give a construction of two-sided invariant metrics on free products (possibly with amalgamation) of groups with two-sided invariant metrics and, under certain conditions, on HNN extensions of such groups. Our approach is similar to the Graev's construction of metrics on free groups over pointed metric spaces.

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Additional Information

Konstantin Slutsky
Affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetspark- en 5, DK-2100 København Ø, Denmark

Keywords: Graev metric, free product, HNN extension
Received by editor(s): May 14, 2012
Received by editor(s) in revised form: October 7, 2012, and October 28, 2012
Published electronically: June 25, 2014
Additional Notes: The author’s research was supported in part by grant no. 10-082689/FNU from Denmark’s Natural Sciences Research Council and by UIUC Research Board Grant.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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