Transverse invariant as Khovanov skein spectrum at its extreme Alexander grading

Nilangshu Bhattacharyya; Adithyan Pandikkadan

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arXiv · 2507.12882

Transverse invariant as Khovanov skein spectrum at its extreme Alexander grading

Nilangshu Bhattacharyya·Adithyan Pandikkadan

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Abstract

We develop a space-level formulation of Khovanov skein homology by constructing a stable homotopy type for annular links. We explicitly define a cover functor from the skein flow category to the cube flow category, thereby establishing the Khovanov skein spectrum. This spectrum extends the framework of Lipshitz and Sarkar's Khovanov spectrum and provides new avenues for understanding transverse link invariants in the annular setting. Furthermore, we establish a map from the Khovanov spectrum to the Khovanov skein spectrum, which, at extreme gradings, recovers the cohomotopy transverse invariant defined by Lipshitz, Ng, and Sarkar.

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Nilangshu Bhattacharyya, Adithyan Pandikkadan. 2025-07-17. Transverse invariant as Khovanov skein spectrum at its extreme Alexander grading. https://arxiv.org/abs/2507.12882

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