Topology Seminar Series
(Conferences / Seminars / Lectures)
Title: Involutions and Floer Homology-1 more information...
Speaker: Kristen Hendricks, MSU
In this set of lectures, we will discuss equivariant (mostly Z_2, with occasional digressions into other groups) versions of several theories collected on the term 'Floer homology.' The first two lectures will focus on equivariant Lagrangian Floer cohomology. We will first do a quick review of ordinary equivariant cohomology, give an abbreviated introduction to Lagrangian Floer cohomology, and discuss some of the technical issues involved in constructing equivariant versions of same. We will then go over two major approaches to resolving these technical difficulties, with some examples and applications of each to such theories as Heegaard Floer homology and symplectic Khovanov homology. The third lecture will take a slightly different tack and focus on equivariant versions of Seiberg-Witten Floer homology (and, eventually, its analog Heegaard Floer homology) with applications to the homology cobordism groups. We will talk briefly about the structure of the integer homology cobordism group, and then discuss Manolescu's use of a Pin(2)-equivariant version of Seiberg-Witten Floer homology to resolve the Triangulations Conjecture. Finally, we will then discuss additional recent applications of the same ideas, including the use of an involution on Heegaard Floer homology to construct an 'involutive' theory analogous to Z_4-Seiberg Witten Floer homology.