We study the Dehn function at infinity in the mapping class group, finding a
polynomial upper bound of degree four. This is the same upper bound that holds
for arbitrary right-angled Artin groups.Comment: 7 pages, 2 figures; this note presents a result which was contained
  in an earlier version of "Pushing fillings in right-angled Artin groups"
  (arXiv:1004.4253) but is independent of the techniques in that pape

Abrams, Aaron

Brady, Noel

Dani, Pallavi

Duchin, Moon

Young, Robert

English

arXiv

LSU Scholarly Repository (Louisiana State Univ.)

Filling loops at infinity in the mapping class group

Aaron Abrams

Noel Brady

Pallavi Dani

Moon Duchin

Robert Young

Crossref

The Michigan Mathematical Journal

Abstract. We study the Dehn function at infinity in the mapping class group, finding a polynomial upper bound of degree four. This is the same upper bound that holds for arbitrary right-angled Artin groups. Dehn functions quantify simple connectivity. That is, in a simply-connected space, every closed curve is the boundary of some disk; the Dehn function measures the area required to fill the curves of a given length. The growth of the Dehn function is invariant under quasi-isometry, so one can define the Dehn function not just for spaces, but also for groups. The Dehn function is not the only group invariant based on a filling problem; for example, one can also define the Dehn function at infinity, which is a quasi-isometry invariant that measures the difficulty of filling closed curves with disks that avoid a large ball. The Dehn function at infinity is a special case (k = 1) of the higher divergence functions Divk that were defined for groups in [?] and serve to quantify the connectivity at infinity. In that paper we survey some results using the growth rates of Divk to detect geometric features of groups and spaces

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FILLING LOOPS AT INFINITY IN THE MAPPING CLASS GROUP

https://digitalcommons.lsu.edu/cgi/viewcontent.cgi?article=1218&context=mathematics_pubs

Filling loops at infinity in the mapping class group

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