Mahan, M. J. (2009) Mapping class groups and interpolating complexes: rank Journal of the Ramanujan Mathematical Society, 24 (4). pp. 341-357. ISSN 0970-1249
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Official URL: http://maths.rkmvu.ac.in/~mahan/intcx.pdf
Abstract
Abstract. A family of interpolating graphs C(S, ξ) of complexity ξ is constructed for a surface S and -2 ≤ ξ ≤ ξ(S). For ξ = -2,-1, ξ (S) -1 these specialize to graphs quasi-isometric to the marking graph, the pants graph and the curve graph respectively. We generalize the notion of a hierarchy and Theorems of Brock-Farb and Behrstock-Minsky to show that the rank of C(S, ξ) is rξ, the largest number of disjoint copies of subsurfaces of complexity greater than ξ that may be embedded in S. The interpolating graphs C(S, ξ) interpolate between the pants graph and the curve graph.
Item Type: | Article |
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Source: | Copyright of this article belongs to Ramanujan Mathematical Society, Madras, India. |
ID Code: | 89539 |
Deposited On: | 28 Apr 2012 12:56 |
Last Modified: | 19 May 2016 04:04 |
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