This will be a research talk, unrelated to the main topics of the seminar. We will discuss the concept of categorification, with Khovanov homology as our main example. We generalize the technique used in the cube construction of Khovanov homology and discuss how to obtain homology theories from functors on posets (one can also view these as quiver representations or as sheaves on finite topological spaces). We show how such homology theories can be used to categorify topological/combinatorial invariants which admit formulas as rank alternating sums over ranked posets, and examine why such invariants are ubiquitous in combinatorics and topology. The complexes associated to posets under this construction are very large. Conditions on posets are discussed under which we are able to significantly cut down the size of these complexes.
Thin Posets and Categorification
15.10.2019 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: