Properties and applications of involutive Heegaard Floer homology

Abstract: Involutive Heegaard Floer homology is a refinement of Heegaard Floer homology. We will extend some properties (naturality, surgery exact triangle) of Heegaard Floer homology to the involutive setting. As an application, we prove a new result about the homology cobordism group (namely, that it is not generated by Seifert fibered spaces). This is joint work with K. Hendricks, M. Stoffregen, and I. Zemke.