Exponential growth of colored HOMFLY-PT homology

Paul Wedrich

doi:10.1016/j.aim.2019.06.023

Exponential growth of colored HOMFLY-PT homology

Paul Wedrich^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

We define reduced colored gl_N link homologies and use deformation spectral sequences to characterize their dependence on color and rank. We then define reduced colored HOMFLY-PT homologies and prove that they arise as large N limits of gl_N homologies. Together, these results allow proofs of many aspects of the physically conjectured structure of the family of type A link homologies. In particular, we verify a conjecture of Gorsky, Gukov and Stošić about the growth of colored HOMFLY-PT homology.

Original language	English
Pages (from-to)	471-525
Number of pages	55
Journal	Advances in Mathematics
Volume	353
DOIs	https://doi.org/10.1016/j.aim.2019.06.023
Publication status	Published - 7 Sept 2019

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10.1016/j.aim.2019.06.023

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title = "Exponential growth of colored HOMFLY-PT homology",

abstract = "We define reduced colored glN link homologies and use deformation spectral sequences to characterize their dependence on color and rank. We then define reduced colored HOMFLY-PT homologies and prove that they arise as large N limits of glN homologies. Together, these results allow proofs of many aspects of the physically conjectured structure of the family of type A link homologies. In particular, we verify a conjecture of Gorsky, Gukov and Sto{\v s}i{\'c} about the growth of colored HOMFLY-PT homology.",

keywords = "Deformation, HOMFLY-PT, Khovanov homology, Knot homology, Spectral sequence",

author = "Paul Wedrich",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

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AU - Wedrich, Paul

PY - 2019/9/7

Y1 - 2019/9/7

N2 - We define reduced colored glN link homologies and use deformation spectral sequences to characterize their dependence on color and rank. We then define reduced colored HOMFLY-PT homologies and prove that they arise as large N limits of glN homologies. Together, these results allow proofs of many aspects of the physically conjectured structure of the family of type A link homologies. In particular, we verify a conjecture of Gorsky, Gukov and Stošić about the growth of colored HOMFLY-PT homology.

AB - We define reduced colored glN link homologies and use deformation spectral sequences to characterize their dependence on color and rank. We then define reduced colored HOMFLY-PT homologies and prove that they arise as large N limits of glN homologies. Together, these results allow proofs of many aspects of the physically conjectured structure of the family of type A link homologies. In particular, we verify a conjecture of Gorsky, Gukov and Stošić about the growth of colored HOMFLY-PT homology.

KW - Deformation

KW - HOMFLY-PT

KW - Khovanov homology

KW - Knot homology

KW - Spectral sequence

UR - https://www.scopus.com/pages/publications/85069586793

U2 - 10.1016/j.aim.2019.06.023

DO - 10.1016/j.aim.2019.06.023

M3 - Article

SN - 0001-8708

VL - 353

SP - 471

EP - 525

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Exponential growth of colored HOMFLY-PT homology

Abstract

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