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Title: Evaluations of annular Khovanov–Rozansky homology
Abstract We describe the universal target of annular Khovanov–Rozansky link homology functors as the homotopy category of a free symmetric monoidal linear category generated by one object and one endomorphism. This categorifies the ring of symmetric functions and admits categorical analogues of plethystic transformations, which we use to characterize the annular invariants of Coxeter braids. Further, we prove the existence of symmetric group actions on the Khovanov–Rozansky invariants of cabled tangles and we introduce spectral sequences that aid in computing the homologies of generalized Hopf links. Finally, we conjecture a characterization of the horizontal traces of Rouquier complexes of Coxeter braids in other types.  more » « less
Award ID(s):
1760329
PAR ID:
10465207
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Mathematische Zeitschrift
Volume:
303
Issue:
1
ISSN:
0025-5874
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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