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- Thomas Jefferson National Accelerator FacilityUS402 papers
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6 papers · 2 filters
3-Manifolds, tangles and persistent invariants
Jozef H. Przytycki, Daniel S. Silver, Susan G. Williams
New obstructions for embedding one compact oriented 3-manifold in another are given. A theorem of D. Krebes concerning 4-tangles embedded in links arises as a special case. Algebra…
Search for different links with the same Jones' type polynomials: Ideas from graph theory and statistical mechanics
Jozef H. Przytycki
We describe in this talk three methods of constructing different links with the same Jones type invariant. All three can be thought as generalizations of mutation. The first combin…
From 3-moves to Lagrangian tangles and cubic skein modules
Jozef H. Przytycki
We discuss several open problems in classical Knot Theory and we develop techniques that allow us to study them: Lagrangian tangles, skein modules and Burnside groups.
Symmetric knots and billiard knots
Jozef H. Przytycki
Symmetry of geometrical figures is reflected in regularities of their algebraic invariants. Algebraic regularities are often preserved when the geometrical figure is topologically…
Torsion of the Khovanov homology
Alexander N. Shumakovitch
Khovanov homology is a recently introduced invariant of oriented links in . It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic o…
The topological interpretation of the core group of a surface in S^4
Jozef H. Przytycki, Witold Rosicki
We give a topological interpretation of the core group invariant of a surface embedded in S^4. We show that the group is isomorphic to the free product of the fundamental group of…