February 2014 - Mdtop - mathdept.okstate.edu

Topology Seminar Thursday
by Odonnol, Danielle Odonnol 24 Feb '14

24 Feb '14

Hello Topologist and Friends, We are please to have Topology Seminar this Thursday (MSCS 514 at 3:30) given by Jeremy Van Horn-Morris form University of Arkansas. Title: A survey of the mapping class group in contact and symplectic topology Abstract: The past roughly twenty years in the study of contact 3-manifolds and symplectic 4-manifolds has been strongly influenced by work of Donaldson, Gompf and Giroux. These tools encode the differential geometric, and differential topological information coming from a contact or symplectic structure through the topological structure of an open book decomposition -- that is, a nicely fibered link. Many interesting properties of a contact structure are detectable in the monodromy maps of these fibrations. We'll introduce some of these properties (such as tight, and fillable) and connect their monodromy characterizations to properties of mapping classes previously studied in topology, and survey some of the recent applications and current interesting questions.

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Topology Seminar Thursday the 20th
by Odonnol, Danielle Odonnol 17 Feb '14

17 Feb '14

Hello Topologists and Friends of Topology, We will have a seminar this Thursday (MSCS 514 at 3:30) given by our very own Trent Schirmer. Title: Splittings of 3-manifolds versus splittings of groups. Abstract: Recent work of mine and Jesse's has shown that "high distance" free decomposing surfaces properly embedded in 3-manifolds with non-empty boundary exert considerable control over the appearance of other incompressible surfaces and Heegaard splittings in the manifold. These incompressible surfaces induce presentations of the fundamental group of the three manifold as a free product amalgamated over a subgroup whose word length is ``persistently" large with respect to a minimal generating set of each of the factors. I discuss the meaning of this.

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No Seminar this Thrusday
by Odonnol, Danielle Odonnol 10 Feb '14

10 Feb '14

Hello Topologists and Friends, There will be no Topology Seminar this week. There is a Thursday Colloquium. Cheers, Danielle

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Topology Seminar: Change of speaker this Thursday
by Odonnol, Danielle Odonnol 05 Feb '14

05 Feb '14

Hello Topologist and Friends, Shelly Harvey has cancelled her visit, due to illness. Henry has graciously offered to speak. We will have a seminar this Thursday (MSCS 514 at 3:30) given by our own Henry Segerman. Title: Structure on the set of triangulations

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Topology Seminar on Thursday
by Odonnol, Danielle Odonnol 03 Feb '14

03 Feb '14

Dear Topologists and Friends of Topology, We will have a seminar this Thursday (MSCS 514 at 3:30) given by Shelly Harvey, from Rice University. Title: Metric Aspects of Knot Concordance Abstract: We are interested in the set of knot up to concordance, denoted C. C is an abelian group but its structure is not very well understood. We propose a new approach to understanding C, namely considering C as a metric space on which there exists many natural operators. Since one example of such an operator is connected-sum with a fixed knot, this approach is arguably more general than focusing on C as an abelian group. In fact, it was previously suggested by the authors along with C. Leidy that C is a fractal space and the proposed self-similarities of C are classical satellite operations. Very recently, Cochran-Davis-Ray proved that many of these satellite operators (strong winding number 1) are indeed injective, modulo the smooth 4-dimensional Poincare Conjecture . We show that that these operators are, in fact, isometric embeddings while winding number zero satellite operators are, by contrast, approximate contractions. This is joint work with Tim Cochran.

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