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DTSTAMP:20251220T020633Z
DESCRIPTION:Title: Strong contractibility in the mapping class group.\n\nTh
 e mapping class group of a compact surface $S$\, denoted $MCG(S)$\, is the
  group of isotopy classes of elements of $Homeo^{+}(S\, partial S)$\, wher
 e isotopies are required to fix the boundary pointwise. The complex of cur
 ves\, $C(S)$\, is a simplicial complex where the vertices are free isotopy
  classes of essential simple closed curves in $S$ and there is an edge con
 necting two vertices if the isotopy classes have geometric intersection nu
 mber zero. Choosing a generating set defines a word metric on the mapping 
 class group. By using the combinatorial properties of $C(S)$ along with th
 e action of $MCG(S)$ on $C(S)$ we are able to study the geometry of the ma
 pping class group. Previously\, Masur and Minsky constructed quasi-geodesi
 cs in $MCG(S)$\, but not much is known about geodesics. In joint work with
  Kasra Rafi\, we have found some explicit examples of geodesics\, denoted 
 $gamma$\, in $MCG(S_{0\,5})$\, where $S_{0\,5}$ is the five-times puncture
 d sphere. We were able to find these geodesics by having constructed an ap
 propriate generating set and having found a homomorphism from $MCG(S_{0\,5
 })$ to $mathbb{Z}$. In addition\, we have constructed a pseudo-Anosov map 
 whose axis is not strongly contracting. A geodesic is strongly contracting
  if its nearest point projection takes disjoint balls from the geodesic to
  sets of bounded diameter\, where the bound should be independent of the b
 all. Strongly contracting geodesics show up in the study of growth tightne
 ss\, for example\, the strongly contracting property was used to prove gro
 wth tightness for actions on non relatively hyperbolic spaces in work by G
 . Arzhantseva\, C. Cashen\, J. Tao\, which is why we pursued this result.
 \n
DTSTART:20180411T190000Z
DTEND:20180411T200000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Yvon Verberne\, University of Toronto
URL:/mathstat/channels/event/yvon-verberne-university-
 toronto-286401
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