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On Asymptotic Dimension of Groups Acting on Trees |
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| Authors: | G Bell A Dranishnikov |
| Institution: | (1) Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, KY, 40292, U.S.A;(2) Department of Mathematics, University of Florida, PO Box 118105, 358 Little Hall, Gainesville, FL, 32611-8105, U.S.A |
| Abstract: | We prove the following.THEOREM. Let  be the fundamental group of a finite graph of groups with finitely generated vertex groups
G
v
having asdim G
v
 n
for all vertices v. Then asdim n+1.This gives the best possible estimate for the asymptotic dimension of an HNN extension and the amalgamated product. |
| Keywords: | amalgamated free product asymptotic dimension graph of groups HNN extension |
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