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Knot Equivalence
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Knot Polynomials from Chern-Simons Field Theory and Their String Theoretic Implications by P. Ramadevi
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- 1 Outline
- 2 Just like Periodic Table of chemical elements
- 3 Periodic table of Knots
- 4 Knot Equivalence
- 5 Knot Invariant through recursive method
- 6 Jones Polynomial
- 7 Chern-Simons Theory
- 8 Well-Known polynomials from Chern-Simons
- 9 Knot Invariants from Chern-Simons
- 10 Example: Trefoil invariant
- 11 Eigenbasis of Braiding operator
- 12 Polynomial invariant of trefoil
- 13 Trefoil evaluation continued
- 14 Figure 8 knot invariant
- 15 Broad classification of knots
- 16 Arborescent Knots
- 17 10152 and 1071 arborescent knots
- 18 Building blocks
- 19 Equivalent Building Blocks
- 20 Arborescent knot- Feynman diagram analogy
- 21 Family Approach: Arborescent knots
- 22 Arborescent knot invariants
- 23 Do we know duality matrix elements
- 24 Detection of Mutation
- 25 [2,1] colored HOMFLY-PT
- 26 Additional information in mixed representation
- 27 Mutation operation on two-tangles
- 28 Tangle and its My mutation
- 29 Knot invariant for the mutant pair
- 30 Knot Polynomials
- 31 Reasons for Integer coefficients
- 32 Khovanov Homology
- 33 Chain Complex
- 34 The vector space
- 35 Homological Invariant
- 36 Gauge-string duality in topological strings
- 37 Duality in topological strings
- 38 Topological String duality contd
- 39 Open topological string amplitudes
- 40 N integers from knot polynomials
- 41 VERIFICATION USING KNOT INVARIANTS
- 42 Can we write InZ [M] as closed string expansion?
- 43 InZM contd
- 44 Subtle Issues
- 45 Generalization of the duality to SO gauge groups
- 46 Oriented contribution
- 47 Witten's Intersecting brane Construction
- 48 Witten's intersecting brane constructioncontd
- 49 M-Theory description of Witten's model
- 50 Sourcing 0 term
- 51 Model A: Witten model
- 52 Two NS5-branes with relative orientation from Witten model
- 53 Relation to Ooguri-Vafa model
- 54 M-Theory description dual to Ooguri-Vafa
- 55 Summary and Open problems
- 56 Q&A
