• Corpus ID: 119656713

Cohomology of the tetrahedral complex and quasi-invariants of 2-knots

@article{Korepanov2015CohomologyOT,
  title={Cohomology of the tetrahedral complex and quasi-invariants of 2-knots},
  author={Igor G. Korepanov and Georgy I. Sharygin and Dmitry V. Talalaev},
  journal={arXiv: Mathematical Physics},
  year={2015}
}
This paper explores a particular statistical model on 6-valent graphs with special properties which turns out to be invariant with respect to certain Roseman moves if the graph is the singular point graph of a diagram of a 2-knot. The approach uses the technic of the tetrahedral complex cohomology. We emphasize that this model considered on regular 3d-lattices appears to be integrable. We also set out some ideas about the possible connection of this construction with the area of topological… 

Zamolodchikov Tetrahedral Equation and Higher Hamiltonians of 2d Quantum Integrable Systems

The main aim of this work is to develop a method of constructing higher Hamiltonians of quantum integrable systems associated with the solution of the Zamolodchikov tetrahedral equation. As opposed

References

SHOWING 1-10 OF 14 REFERENCES

Cohomologies of n-simplex relations

Abstract A theory of (co)homologies related to set-theoretic n-simplex relations is constructed in analogy with the known quandle and Yang–Baxter (co)homologies, with emphasis made on the tetrahedron

Reidemeister-type moves for surfaces in four-dimensional space

We consider smooth knottings of compact (not necessarily orientable) n-dimensional manifolds in R (or S), for the cases n = 2 or n = 3. In a previous paper we have generalized the notion of the

Twisting spun knots

1. Introduction. In [5] Mazur constructed a homotopy 4-sphere which looked like one of the strongest candidates for a counterexample to the 4-dimensional Poincaré Conjecture. In this paper we show

Zamolodchikov Tetrahedral Equation and Higher Hamiltonians of 2d Quantum Integrable Systems

The main aim of this work is to develop a method of constructing higher Hamiltonians of quantum integrable systems associated with the solution of the Zamolodchikov tetrahedral equation. As opposed

Topological BF theories in 3 and 4 dimensions

In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2‐knots (in 4 dimensions). The vacuum

Quandle cohomology and state-sum invariants of knotted curves and surfaces

The 2-twist spun trefoil is an example of a sphere that is knotted in 4-dimensional space. A proof is given in this paper that this sphere is distinct from the same sphere with its orientation

Notes on Simplicial Bf Theory

In this work we discuss the construction of " simplicial BF theory " , the field theory with finite-dimensional space of fields, associated to a triangulated manifold, that is in a sense equivalent

Quantum field theory and the Jones polynomial

It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones

Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles

A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.

Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied