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Uniform embeddability and exactness of free products |
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| Authors: | Xiaoman Chen Marius Dadarlat Erik Guentner Guoliang Yu |
| Institution: | a Institute of Mathematics, Fudan University, Shanghai, 200433, People's Republic of China b Department of Mathematics, 1395 Mathematical Sciences Building, Purdue University, West Lafayette, IN 47907-1395, USA c Mathematics Department, University of Hawai‘i, Manoa, 2565 The Mall, Keller 401A, Honolulu, HI 86802, USA d Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA |
| Abstract: | Let A and B be countable discrete groups and let Γ=A∗B be their free product. We show that if both A and B are uniformly embeddable in a Hilbert space then so is Γ. We give two different proofs: the first directly constructs a uniform embedding of Γ from uniform embeddings of A and B; the second works without change to show that if both A and B are exact then so is Γ. |
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