We provide a finite-dimensional categorification of the symmetric evaluation of slN-webs
using foam technology. As an output we obtain a symmetric link homology theory …

In 2005 Dunfield, Gukov and Rasmussen conjectured an existence of the spectral sequence
from the reduced triply graded Khovanov-Rozansky homology of a knot to its knot Floer …

In this paper, we study the skein exact sequence for links via the exact surgery triangle of
link Floer homology and compare it with other skein exact sequences given by Ozsv\'ath and …

Using a modified foam evaluation, we give a categorification of the Alexander polynomial of
a knot. We also give a purely algebraic version of this knot homology which makes it appear …

The one-variable Alexander polynomial. q/2 ZŒq 1 has a myriad of definitions. Among them,
the ones originating in topology are probably the most studied. The Alexander polynomial …

The aim of this thesis is to contribute towards the theory of higher and quantum invariants of
knots. It is divided into two parts. The first part deals with higher invariants, in which we …

Floer homology, introduced by Andreas Floer in 1988, has had a dramatic impact on the
field of lowdimensional topology, particularly via its incarnations as monopole and …