A Formula for Khovanov Type Link Homology of Pretzel Knots (Communications in Mathematical Research, 2021)
Khovanov type homology is a generalization of Khovanov homology.The main result of this paper is to give a recursive formula for Khovanov typehomology of pretzel knots $P(−n, −m, m)$. The computations reveal that therank of the homology of pretzel knots is an invariant of $n$. The proof is basedon a "shortcut" and two lemmas that recursively reduce the computationalcomplexity of Khovanov type homology.
Keywords: pretzel knot; Khovanov type homology; Frobenius algebra; TQFT.