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2011 Volume distortion in groups
Hanna Bennett
Algebr. Geom. Topol. 11(2): 655-690 (2011). DOI: 10.2140/agt.2011.11.655


Given a space Y in X, a cycle in Y may be filled with a chain in two ways: either by restricting the chain to Y or by allowing it to be anywhere in X. When the pair (G,H) acts on (X,Y), we define the k–volume distortion function of H in G to measure the large-scale difference between the volumes of such fillings. We show that these functions are quasi-isometry invariants, and thus independent of the choice of spaces, and provide several bounds in terms of other group properties, such as Dehn functions. We also compute the volume distortion in a number of examples, including characterizing the k–volume distortion of k in kM, where M is a diagonalizable matrix. We use this to prove a conjecture of Gersten.


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Hanna Bennett. "Volume distortion in groups." Algebr. Geom. Topol. 11 (2) 655 - 690, 2011.


Received: 12 February 2010; Revised: 21 December 2010; Accepted: 21 December 2010; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1217.20025
MathSciNet: MR2782540
Digital Object Identifier: 10.2140/agt.2011.11.655

Primary: 20F65
Secondary: 20F67 , 57M07

Keywords: Dehn function , geometric group theory , Subgroup distortion , volume distortion

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.11 • No. 2 • 2011
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