Topology Seminar

The Topology seminar meets on Tuesdays from 2-3:20 pm in room 226 Goldsmith Hall.

Date Speaker 
Nov. 1 Stephen Hermes (Brandeis)
Title:  Homology of branched coverings, with applications to concordance.
Oct. 25 Priyavrat Deshpande (Northeastern).
Title: Reflections on manifolds and related arrangements
Abstract:  An arrangement of hyperplanes is a collection of finitely many hyperplanes in a real vector space. It is known that the combinatorics of the intersections of these hyperplanes contains substantial information about the topology of the complement of the hyperplanes in the real as well as the complexified space. For example, the cohomology of the complexified complement can be expressed in terms of the intersection lattice associated with the arrangement. The face poset of an arrangement defines a simplicial complex (the Salvetti complex) which has the homotopy type of this complement.
In this talk I shall introduce a generalization of hyperplane arrangements to manifolds. I will also define a notion of the tangent bundle complement and present results that describe the homotopy type of this complement in terms combinatorics of the arrangement. Finally, I will also outline attempts to generalize classical work of Deligne on Artin groups to this setting.
Oct. 18 Alyson Burchardt (Brandeis)

Title: Tristram-Levine Signature (continued)
Oct. 11 No seminar (Brandeis Thursday)
Oct. 4 Alyson Burchardt (Brandeis)
Title: Algebraic obstructions to concordance
Abstract:  I will introduce the classical algebraic obstruction arising from the Seifert matrix, and discuss the Tristram-Levine signatures. 
Sept. 27 Daniel Ruberman (Brandeis)
Title: Introduction to knot concordance.
Abstract:  I will give an introduction to knot concordance in the classical dimension. 
Sept. 20 Liam Watson (UCLA)

Title: The bordered invariants of the twisted I-bundle over the Klein bottle.
Abstract: The twisted I-bundle over the Klein bottle is a relatively simple Seifert fibred space with torus boundary. From the standpoint of Heegaard Floer homology this is a very simple manifold, in the sense that all of its non-zero Dehn fillings are L-spaces. It is not the complement of a knot in the three-sphere (or any integer homology sphere, for that matter), and as a result provides a interesting example for studying bordered Floer homology; the aforementioned simplicity is nicely presented in terms of these invariants. The calculation of these invariants play an important role in joint work with Boyer and Gordon, demonstrating that all rational homology spheres admitting Sol geometry are L-spaces. This fact is a key step in establishing that being an L-space is equivalent to having a non-left-orderable fundamental group for all closed, connected, geometric, non-hyperbolic three-manifolds. In discussing some aspects of these results, we'll show how the twisted I-bundle over the Klein bottle may be used to construct large families of toroidal manifolds with 'small' Heegaard Floer homology, some examples of which (though not all) are L-spaces.
Sept. 13
Inanc Baykur (Max Planck Institute, Bonn)

Title: Broken Lefschetz fibrations and smooth four-manifolds


Abstract: In this talk, we are going to discuss a smooth invariant defined for four-manifolds and embeddings of surfaces via generalized fibrations, and present some calculations.