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Title: Knot invariants from Virasoro related representation and pretzel knots

In this study, we remind the method to calculate colored Jones polynomials for the plat representations of knot diagrams from the knowledge of modular transformation (monodromies) of Virasoro conformal blocks with insertions of degenerate fields. As an illustration we use a rich family of pretzel knots, lying on a surface of arbitrary genus g, which was recently analyzed by the evolution method. Further generalizations can be to generic Virasoro modular transformations, provided by integral kernels, which can lead to the Hikami invariants.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. ITEP, Moscow (Russia); Rutgers Univ., Piscataway, NJ (United States)
  2. ITEP, Moscow (Russia); UFRN, Natal (Brazil)
  3. ITEP, Moscow (Russia); Lebdev Physics Institute, Moscow (Russia); National Research Nuclear Univ. MEPhI, Moscow (Russia); Institute for Information Transmission Problems, Moscow (Russia)
  4. ITEP, Moscow (Russia); National Research Nuclear Univ. MEPhI, Moscow (Russia); Institute for Information Transmission Problems, Moscow (Russia)
Publication Date:
Grant/Contract Number:
SC0010008; SC0003883; SC0007897; ARRA-SC0003883
Type:
Published Article
Journal Name:
Nuclear Physics. B
Additional Journal Information:
Journal Volume: 899; Journal Issue: C; Journal ID: ISSN 0550-3213
Publisher:
Elsevier
Research Org:
Rutgers Univ., Piscataway, NJ (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING
OSTI Identifier:
1209581
Alternate Identifier(s):
OSTI ID: 1240267