Graev metrics on free products and HNN extensions
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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.References
- Longyun Ding and Su Gao, Graev metric groups and Polishable subgroups, Adv. Math. 213 (2007), no. 2, 887–901. MR 2332614, DOI 10.1016/j.aim.2007.01.014
- Su Gao, Invariant descriptive set theory, Pure and Applied Mathematics (Boca Raton), vol. 293, CRC Press, Boca Raton, FL, 2009. MR 2455198
- M. I. Graev, On free products of topological groups, Izvestiya Akad. Nauk SSSR. Ser. Mat. 14 (1950), 343–354 (Russian). MR 0036768
- M. I. Graev, Free topological groups, Amer. Math. Soc. Translation 1951 (1951), no. 35, 61. MR 0038357
- G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 6th ed., Oxford University Press, Oxford, 2008. Revised by D. R. Heath-Brown and J. H. Silverman; With a foreword by Andrew Wiles. MR 2445243
- Graham Higman, B. H. Neumann, and Hanna Neumann, Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247–254. MR 32641, DOI 10.1112/jlms/s1-24.4.247
- Alexander S. Kechris, Topology and descriptive set theory, Topology Appl. 58 (1994), no. 3, 195–222. MR 1288299, DOI 10.1016/0166-8641(94)00146-4
- A. Markoff, On free topological groups, C. R. (Doklady) Acad. Sci. URSS (N. S.) 31 (1941), 299–301. MR 0004634
- A. Markoff, On free topological groups, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 9 (1945), 3–64 (Russian, with English summary). MR 0012301
- O. V. Sipachëva, The topology of a free topological group, Fundam. Prikl. Mat. 9 (2003), no. 2, 99–204 (Russian, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 131 (2005), no. 4, 5765–5838. MR 2056625, DOI 10.1007/s10958-005-0445-z
- O. V. Sipacheva and V. V. Uspenskiĭ, Free topological groups with no small subgroups, and Graev metrics, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 4 (1987), 21–24, 101 (Russian). MR 913066
- Lou van den Dries and Su Gao, A Polish group without Lie sums, Abh. Math. Semin. Univ. Hambg. 79 (2009), no. 1, 135–147. MR 2541347, DOI 10.1007/s12188-009-0019-y
Additional Information
- Konstantin Slutsky
- Affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetspark- en 5, DK-2100 København Ø, Denmark
- MR Author ID: 911581
- Email: kslutsky@gmail.com
- 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.
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 6353-6395
- MSC (2010): Primary 54H11, 03E15
- DOI: https://doi.org/10.1090/S0002-9947-2014-06010-8
- MathSciNet review: 3267013