Colored Jones polynomials and abelianized Lefschetz numbers
DOI10.1016/j.aim.2023.109453arXiv2012.09150OpenAlexW3111977841MaRDI QIDQ6189375
Publication date: 8 February 2024
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.09150
configuration spacesbraidsLefschetz numbersNielsen fixed point theorytwisted homologyquantum invariants of knots
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Discriminantal varieties and configuration spaces in algebraic topology (55R80) Fixed points and coincidences in algebraic topology (55M20) Knot polynomials (57K14) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) Knot theory (57K10) Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) (57K18)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Categorified \(\mathfrak{sl}_N\) invariants of colored rational tangles
- The Lawrence-Krammer-Bigelow representations of the braid groups via \(U_q(\mathfrak{sl}_2)\).
- The hyperbolic volume of knots from the quantum dilogarithm
- Homological representations of the Hecke algebra
- The generalized Lefschetz number of homeomorphisms on punctured disks
- Topology of the complement of real hyperplanes in \({\mathbb C}^ N\)
- Homology of a local system on the complement of hyperplanes
- A relative generalized Lefschetz number
- Singular homology and cohomology with local coefficients and duality for manifolds
- On Khovanov's categorification of the Jones polynomial
- A note on the Lawrence-Krammer-Bigelow representation
- Manifold-theoretic compactifications of configuration spaces
- The homotopy type of Artin groups
- Cohomology of Artin groups
- An integral form of the quantized enveloping algebra of \(sl_2\) and its completions
- Grid diagrams and Khovanov homology
- Relative fixed point theory
- A homological definition of the HOMFLY polynomial
- Nilpotent slices, Hilbert schemes, and the Jones polynomial
- Centerless groups -- an algebraic formulation of Gottlieb's theorem
- A homological model for \(U_q\mathfrak{sl}(2)\) Verma modules and their braid representations
- Theory of Hypergeometric Functions
- Finite Dimensional Hopf Algebras Arising From Quantized Universal Enveloping Algebras
- Lectures on Nielsen fixed point theory
- A polynomial invariant for knots via von Neumann algebras
- Universal Cover of Salvetti's Complex and Topology of Simplicial Arrangements of Hyperplanes
- CATEGORIFICATIONS OF THE COLORED JONES POLYNOMIAL
- Generalized Lefschetz Numbers
- Topological formula of the loop expansion of the colored Jones polynomials
- A REFLEXIVE REPRESENTATION OF BRAID GROUPS
- Braid groups are linear
- The colored Jones polynomials and the simplicial volume of a knot
This page was built for publication: Colored Jones polynomials and abelianized Lefschetz numbers
