The Heegaard Floer homology for a knots, link and 3-manifold with boundaryAbstract
On the presupposition that Heegaard Floer homology (HF) for a closed 3-
manifold has been introduced, in this talk, we will review the
definition of the HF for a link and knot and its properties. This
definition turns out to be a special case of the HF for a 3-manifold
with boundary. If time allows, we will briefly introduce the definition
of the HF for a 3-manifold with boundary (mainly sutured Floer homology
and bordered Floer homology).
The Alexander polynomial of the balanced bipartite graphAbstract
The Alexander polynomial is one of the most classical knot invariants.
It has both classical and modern interpretations. In classical case for
example, it can be defined from the universal abelian covering of the
knot complement, while in modern case, it has super sl(1, 1) model,
Burau representation model etc. For a balanced bipartite graph, we
defined its Heegaard Floer homology, and we call its Euler
characteristic the Alexander polynomial of the graph. In this talk, we
aim to discuss different interpretations of this polynomial.