Zobrazeno 1 - 10
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pro vyhledávání: '"Korepanov, I. G."'
Autor:
Korepanov, I. G.
"Nonconstant cohomologies" are introduced for solutions of set-theoretical four-simplex equation (FSE). While usual cohomologies lead to solutions of constant quantum FSE, our "nonconstant cohomologies" lead to solutions of nonconstant quantum FSE. C
Externí odkaz:
http://arxiv.org/abs/1601.04063
Autor:
Korepanov, I. G.
A simple ansatz is proposed for two-color R-matrix satisfying the tetrahedron equation. It generalizes, on one hand, a particular case of the eight-vertex model to three dimensions, and on another hand - Hietarinta's permutation-type operators to the
Externí odkaz:
http://arxiv.org/abs/1601.00794
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 t
Externí odkaz:
http://arxiv.org/abs/1510.03015
Autor:
Korepanov, I. G.
Relatively simple algebraic relations are presented corresponding to Pachner moves 3 -> 3 and 2 <-> 4, thus providing two thirds of the foundation for a four-dimensional topological quantum field theory. These relations are written in terms of Grassm
Externí odkaz:
http://arxiv.org/abs/0911.1395
Autor:
Bel'kov, S. I., Korepanov, I. G.
Publikováno v:
Theor. Math. Phys. 163:3, 819-830 (2010)
We construct a solution to pentagon equation with anticommuting variables living on two-dimensional faces of tetrahedra. In this solution, matrix coordinates are ascribed to tetrahedron vertices. As matrix multiplication is noncommutative, this provi
Externí odkaz:
http://arxiv.org/abs/0910.2082
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
Comment: 27 pages
Comment: 27 pages
Externí odkaz:
http://arxiv.org/abs/0907.3787
Autor:
Korepanov, I. G.
Publikováno v:
Theor. Math. Phys. 158:1 (2009) 82-95
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a manifold with a
Externí odkaz:
http://arxiv.org/abs/0803.0123
Autor:
Korepanov, I. G.
Publikováno v:
SIGMA 1 (2005), 021, 7 pages
Pachner move 3 ->3 deals with triangulations of four-dimensional manifolds. We present an algebraic relation corresponding in a natural way to this move and based, a bit paradoxically, on three-dimensional geometry.
Comment: Published in SIGMA (
Comment: Published in SIGMA (
Externí odkaz:
http://arxiv.org/abs/math/0510095
Autor:
Korepanov, I. G.
We construct knot invariants on the basis of ascribing Euclidean geometric values to a triangulation of sphere S^3 where the knot lies. The main new feature of this construction compared to the author's earlier papers on manifold invariants is that n
Externí odkaz:
http://arxiv.org/abs/math/0405547
Autor:
Korepanov, I. G.
Publikováno v:
Theor. Math. Phys. 138, no. 1 (2004) 18--27
Building on a classical solution to the pentagon equation, constructed earlier by the author and E.V. Martyushev and related to the flat geometry invariant under the group SL(2), we construct an algebraic complex corresponding to a triangulation of a
Externí odkaz:
http://arxiv.org/abs/math/0304149