April 2013 - Mdtop - mathdept.okstate.edu

Seminar today
by Jesse Johnson 18 Apr '13

18 Apr '13

Dear Topologists and Friends of Topology, Bo-hyun will be giving today's seminar talk at 3:30 in MSCS 514. Title: An Algorithm to detect three bridge knots which are in bridge positions Abstract: The Bracket Polynomial is invariant under a regular isotopy but it is not isotopy invariant because it is not invariant under a type I Reidemeister move. Kauffman, however, found Kauffman Polynomial by that would make the polynomial isotopy invariant and make the polynomial equivalent to the Jones Polynomial. I would like to present a way to calculate the Kauffman Polynomial of two bridge presentation knots and three bridge presentation knots by using four $2\times 2$ matrices and eight $5\times 5$ matrices respectively. This one can help us to detect three bridge knots which are in three bridge position.

1 0

Seminar Tomorrow
by Jesse Johnson 10 Apr '13

10 Apr '13

Dear Topologists and Friends of Topology, Will Cavendish from Oxford University will be giving the seminar talk tomorrow (Thursday) at 3:30 in MSCS 514. Title: Topological methods for engulfing subgroups Abstract: Given a group $G$ and a subgroup $H$, $H$ is said to be engulfed in $G$ if $H$ can be distinguished from $G$ by looking at maps to finite groups, i.e. if there exists a homomorphism $\phi:G \to F$ where $F$ is finite and $\phi(H)\ne \phi(G)$. In this talk, we will discuss some of the topological applications of engulfing in the context of 3-manifold theory, and then demonstrate how engulfing can be understood in terms of the cohomology of interesting topological spaces called solenoids.

1 0

Seminar this afternoon
by Jesse Johnson 04 Apr '13

04 Apr '13

Dear Topologists and Friends of Topology: Trent will give the topology seminar this afternoon at 3:30 in MSCS 514. Sorry for the late notice - I just posted this on announce and in the lounge yesterday. Also, because of the MAA meeting tomorrow, I'm not sure if the reading group should still meet at the usual time. If you've been attending the group, but there is an MAA event you plan to attend instead tomorrow, let me know. If there are enough people planning to miss it, I will send an e-mail to cancel the reading group meeting. (If you DON'T hear from me, we will still meet Friday afternoon at 2:30.) Title: High Distance Free Decompositions Abstract: Free decompositions were introduced by Kobayashi about a decade or so ago to construct pairs of knots whose tunnel number degenerates under connected sum. I inject some curve complex juices into them to construct knots with "High Distance Free Decompositions." Such knots have many interesting properties relating to their Heegaard structure, dehn surgery, and yes, the behavior of tunnel number under connected sum. This is joint work with Jesse.

1 0