Topology Seminar 2013--2014 Archive

Speaker: Ken Baker (U. Miami)

Title:Links of divides vs. L-space knots
 
Abstract: Yamada has shown that all known knots with Dehn surgeries to lens spaces have presentations as A'Campo's links of divides. Is this true for all knots with Dehn surgeries to L-spaces, the L-space knots? L-spaces are the Heegaard Floer generalization of lens spaces, and L-space knots are known to have many of the basic properties of links of divides. While the sets of links of divides and have a substantial intersection with the set of L-space knots, neither contains the other. We highlight their distinctions by examining their relationships with cabling and satellite operations.
 
Date:Friday, May 16th
 
Location: DSB C114
 

Speaker: Sam Churchill
 
Title:  Turaev reconstruction theorem
 
Abstract: This is a key theorem in setting up a combinatorial language for describing smooth 4-manifolds.   If one thinks of 2-dimensional manifolds as having a graph as a "spine", Turaev's language has a generic 2-dimensional complex as its "spine".  This is the formalism Sam will set up. 
 
Date: Friday April 11th.  3-4pm.
 
Location: DSB C128. 

Speaker: Robin Koytcheff
 
Title: Spaces of knots.
 
Abstract: In short, much of Robin and my own work on spaces of knots has to do with the overlap of operads acting on knot spaces and the "functor calculus" way of looking at the homotopy type of knot spaces.  Robin's talk is part of an effort to merge the two understandings, building operad actions on the embedding tower associated to embedding spaces. 
 

Date: Friday March 7th. 3-4pm.

Location: DSB C128.


Speaker: Ryan Budney

Title: A coming census of triangulated smooth 4-manifolds.

Abstract: I will talk about a census of triangulated 4-manifolds, algorithmically recognising 4-manifolds and a procedure to determine if a 4-manifold fibres over the circle. 
 
Date: Friday February 21st, 3-4pm.
 
Location: DSBC128.

Speaker: Sam Churchill

Title: 4-manifolds bounding 3-manifolds

Date: Friday October 4th, 3pm-4pm

Location: CLE A211


Speaker: Joseph Cheng (UBC)

Title: Poincare duality for orbifolds in Morava K-theory

Abstract: It was showed by Greenlees and Sadofsky that the classifying spaces of finite groups are self-dual with respect to Morava K-theory K(n). Their duality map was constructed using a transfer map. I will describe the map and its generalization which would induce a K(n)-version of Poincare duality for classifying spaces of orbifolds. Some examples of K(n)-fundamental class and intersection product will be given. If time permits, I will explain the similarity of this duality map with that of the Spanier-Whitehead duality for manifolds from the point of view of differentiable stacks.

Date: Friday September 27th

Time: 3pm--4pm

Location: CLE A211


Speaker: Robin Koytcheff

Title: A coloured operad for string link infection

Abstract: This talk builds on the work of Budney on operads and knot spaces described in the past two seminars. In particular, we build on his operad for splicing of knots, which we will briefly review. Infection of knots or links by string links is a generalization of splicing from knots to links and is useful for studying concordance of knots. In joint work with Burke, we have constructed a coloured operad that encodes this infection operation. This work has motivated us to prove a prime decomposition for 2-component string links in joint work with Burke and Blair. This suggests the possibility of proving further decomposition theorems analogous to those of Budney; this last item is work in progress.

Date: Friday September 13th

Time: 3pm-4pm

Location: CLE A211


Speaker: Ryan Budney

Title: Spaces of embeddings. Part 1 of 2

Abstract: I will describe recent work on the homotopy-type of spaces of embeddings, primarily the space of embeddings of the circle in the 3-sphere. The talk will consist of an introduction to operads, and the basics of what is known about knots and embedding spaces. I will describe how Schubert's connect-sum decomposition can be elaborated into an action of the 2-cubes operad on knot spaces, and how that relates to the homotopy-type of knot spaces via geometrization. This inspired a further operad called the splicing operad, which has further insights into the topology of knot spaces, and deeper connections to geometrization. Towards the end of this 2-part talk I will discuss how there appears to be nice connections to the tools coming from the calculus of functors for describing embedding spaces.

Date: Friday August 23rd

Time: 3pm-4pm

Location: CLE A211


Speaker: Ryan Budney

Title: Spaces of embeddings. Part 2 of 2

Abstract: See previous talk.

Date: Friday August 30th, 3pm-4pm

Location: CLE A211