Seminar| Institute of Mathematical Sciences
Time: Thursday, June 11th, 2026,15:30-16:30
Location: IMS R408
Speaker: Yonghan Xiao, Peking University
Abstract:Recently, investigation on real manifolds of low dimension became increasing popular since the development of the real Seiberg-Witten Floer homotopy type (Konno-Miyazawa-Taniguchi) and the real monopole Floer homology (Jiakai Li). Last year, their Heegaard Floer theoretic counterpart was developed by Guth and Manolescu. In this talk, we introduce its knot version- real knot Floer homology for strongly invertible knots and links. When the underlying manifold is S^3, it admits a combinatorial description. Using this, we analyze basic structural properties of the theory and provide bounds for equivariant unknotting number and smooth slice genus. We also show two different skein exact triangles, leading to a real Alexander polynomial which satisfies a symmetric skein relation. Using the combinatorial description, Zhenkun Li wrote a computer program for this. We will use some examples calculated from it to illustrate the properties of our theory.