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- W3099536498 abstract "We find new bounds on the conformal dimension of small cancellation groups. These are used to show that a random few relator group has conformal dimension $$2 + o(1)$$ asymptotically almost surely (a.a.s.). In fact, if the number of relators grows like $$l^K$$ in the length l of the relators, then a.a.s. such a random group has conformal dimension $$2+K+ o(1)$$ . In Gromov’s density model, a random group at density $$d<frac{1}{8}$$ a.a.s. has conformal dimension $$asymp dl / |log d|$$ . The upper bound for $$C'(frac{1}{8})$$ groups has two main ingredients: $$ell _p$$ -cohomology (following Bourdon–Kleiner), and walls in the Cayley complex (building on Wise and Ollivier–Wise). To find lower bounds we refine the methods of Mackay (Geom Funct Anal 22(1):213–239, 2012) to create larger ‘round trees’ in the Cayley complex of such groups. As a corollary, in the density model at $$d<frac{1}{8}$$ , the density d is determined, up to a power, by the conformal dimension of the boundary and the Euler characteristic of the group." @default.
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- W3099536498 date "2015-06-13" @default.
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- W3099536498 title "Conformal dimension via subcomplexes for small cancellation and random groups" @default.
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- W3099536498 doi "https://doi.org/10.1007/s00208-015-1234-8" @default.
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