Monoids in the braid and mapping class groups from contact topology

Geometry Topology Seminar
Wednesday, April 16, 2014 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Jeremy Van Horn-Morris – University of Arkansas
John Etnyre
A monoidal subset of a group is any set which is closed under the product (and contains the identity). The standard example is Dehn^+, the set of maps whcih can be written as a product of right-handed Dehn twists. Using open book decompositions, many properties of contact 3-manifolds are encoded as monoidal subsets of the mapping class group. By a related construction, contact topology also produces a several monoidal subsets of the braid group. These generalize the notion of positive braids and Rudolphs ideas of quasipositive and strongly quasipositive. We'll discuss the construction of these monoids and some of the many open questions.