On some $p$-differential graded link homologies II

In [QS20], a link invariant categorifying the Jones polynomial at a 2pth root of unity, where p is an odd prime, was constructed. This categorification utilized an N = 2 specialization of a differential introduced by Cautis. Here we give a family of link homologies where the Cautis differential is specialized to a positive integer of the form N = kp+ 2. When k is even, all these link homologies categorify the Jones polynomial evaluated at a 2pth root of unity, but they are non-isomorphic invariants.

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