Seminarium KMMF "Teoria Dwoistości"

We offer gentle introduction to Khovanov homology. We startfrom chain complexes and classical examples of homology (forsimplicial complexes, groups and quandles). We introduce the notion of(pre)simplicial sets (and modules) and (pre)cubic sets (and modules).We show how to construct geometric realization of (pre)simplicial and(pre)cubic sets. We give an elementary definition of Khovanov homologyof links and discuss geometric realization in extreme and almostextreme grading.