English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We introduce a multi-parameter deformation of the triply-gradedKhovanov--Rozansky homology of links colored by one-column Young diagrams,generalizing the "$y$-ified" link homology of Gorsky--Hogancamp and work ofCautis--Lauda--Sussan. For each link component, the natural set of deformationparameters corresponds to interpolation coordinates on the Hilbert scheme ofthe plane. We extend our deformed link homology theory to braids by introducinga monoidal dg 2-category of curved complexes of type $A$ singular Soergelbimodules. Using this framework, we promote to the curved setting thecategorical colored skein relation from arXiv:2107.08117 and also the notion ofsplitting map for the colored full twists on two strands. As applications, wecompute the invariants of colored Hopf links in terms of ideals generated byHaiman determinants and use these results to establish general link splittingproperties for our deformed, colored, triply-graded link homology. Informed bythis, we formulate several conjectures that have implications for the relationbetween (colored) Khovanov--Rozansky homology and Hilbert schemes.

Link splitting deformation of colored Khovanov--Rozansky homology