Top group of knot Floer homology and Murasugi sum

Knot Floer homology is a link invariant introduced by Ozsváth and Szabó that detects fiberedness. Specifically, Ni proved that a link is fibered if and only if the rank of the top group of knot Floer homology is one. It is well-known that fiberedness is preserved under the Murasugi sum operation, so we study the behavior of the top group under Murasugi sum. In this talk, we discuss the development of the study of the top group, especially its interaction with Murasugi sum. This is joint work with Matthew Hedden and Sucharit Sarkar.