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Nguyen D. Duong

Publications and source records attributed to Nguyen D. Duong.

2 recordsLinked to original sources
arXiv2014

Twisting bordered Khovanov homology

We describe a bordered version of totally twisted Khovanov homology. We first twist Roberts's type $D$ structure by adding a "vertical" type $D$ structure which generalizes the vertical map in twisted tangle homology. One of the distinct advantages of our type $D$ structure is that it is homotopy equivalent to a type $D$ structure supported on "spanning tree" generators. We also describe how to twist Roberts's type $A$ structure for a left tangle in such a way that pairing our type $A$ and type $D$ structures will result in the totally twisted Khovanov homology.

math.GT↗
arXiv2012

Twisted skein homology

We apply the techniques of totally twisted Khovanov homology to the constructions by M. Asaeda, J. Przytycki, and A. Sikora of Khovanov type homologies for links and tangles in I-bundles over (orientable) surfaces. As a result we describe an invariant chain complex built out of resolutions with only non-contractible circles. We use these to understand the δ-graded homology for links with alternating projection to the surface.

math.GT↗