Student Topology

We will review basic results about involutive Heegaard Floer homology that will be relevant to our further discussion of corks this quarter.

This quarter we will be reading Corks, involutions, and Heegaard Floer Homology by Dai, Hedden, and Mallick. 

The double-suspension theorem of J.W. Cannon and R.D. Edwards states that the twofold suspension of any homology sphere is homeomorphic to the sphere two dimensions higher. The double suspension theorem implies the existence of many triangulations of spheres of dimension at least 5 which do not…

Last time, we discussed vanishing criteria for skein lasagna modules and introduced the lasagna s-invariant. Now, we will see how the lasagna s-invariant can be used to distinguish smooth 4-manifolds.

We will learn about how to detect exotica by skein lasagna modules.

We will discuss the effect of attaching 2-handles on skein lasagna modules.

We will go over the construction and basic properties of the skein lasagna module of a 4-manifold. We will also discuss the effect of attaching 3-handles on skein lasagna modules.

We begin our study of Skein-Lasagna modules with some background, and the definition.

Student spectral sequences seminar.

Applications of the Adams spectral sequence.