Zobrazeno 1 - 10
of 56
pro vyhledávání: '"Igor G. Korepanov"'
Autor:
Igor G. Korepanov
Publikováno v:
Partial Differential Equations in Applied Mathematics, Vol 11, Iss , Pp 100856- (2024)
A cohomology theory for “odd polygon” relations—algebraic imitations of Pachner moves in dimensions 3, 5, …—is constructed. Manifold invariants based on polygon relations and nontrivial polygon cocycles are proposed. Example calculation res
Externí odkaz:
https://doaj.org/article/9ea7f6b15c04446593a225cc01fdab4f
We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang--Baxter (2-simplex), respectively. We examine the general structure of (2n+1)-gon and 2n-simplex equations in direct sums of vector spa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9267f67df035c1759dea94902ab447cc
http://arxiv.org/abs/2009.02352
http://arxiv.org/abs/2009.02352
Autor:
Igor G. Korepanov
Publikováno v:
Advances in Applied Clifford Algebras. 27:1411-1430
Recently, an algebraic realization of the four-dimensional Pachner move 3--3 was found in terms of Grassmann--Gaussian exponentials, and a remarkable nonlinear parameterization for it, going in terms of a $\mathbb C$-valued 2-cocycle. Here we define,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ad34f90906384495bb8d24a584d5a377
https://doi.org/10.1007/s00006-016-0746-y
https://doi.org/10.1007/s00006-016-0746-y
Autor:
Igor G. Korepanov
A construction of hexagon relations - algebraic realizations of four-dimensional Pachner moves - is proposed. It goes in terms of "permitted colorings" of 3-faces of pentachora (4-simplices), and its main feature is that the set of permitted coloring
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::de405d1aedc8e1ec280daedff9dccc5c
http://arxiv.org/abs/1812.10072
http://arxiv.org/abs/1812.10072
Autor:
Igor G. Korepanov, Nurlan M. Sadykov
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 9, p 053 (2013)
We consider relations in Grassmann algebra corresponding to the four-dimensional Pachner move 3-3, assuming that there is just one Grassmann variable on each 3-face, and a 4-simplex weight is a Grassmann-Gaussian exponent depending on these variables
Externí odkaz:
https://doaj.org/article/3d7d68a774ad4a4b99239770af9b63e2
Autor:
Igor G. Korepanov, Nurlan M. Sadykov
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 9, p 030 (2013)
We construct vast families of orthogonal operators obeying pentagon relation in a direct sum of three n-dimensional vector spaces. As a consequence, we obtain pentagon relations in Grassmann algebras, making a far reaching generalization of exotic Re
Externí odkaz:
https://doaj.org/article/cb94e59e39e74e1bbf472417606c6a70
Autor:
Igor G. Korepanov
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 7, p 117 (2011)
New algebraic relations are presented, involving anticommuting Grassmann variables and Berezin integral, and corresponding naturally to Pachner moves in three and four dimensions. These relations have been found experimentally – using symbolic comp
Externí odkaz:
https://doaj.org/article/ec4e69d2fd184b26a60eaa3da4cbb778
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 6, p 032 (2010)
We present an invariant of a three-dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in
Externí odkaz:
https://doaj.org/article/4786b6acfe3848518f9183a2c3b8452d
Autor:
Igor G. Korepanov
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 1, p 021 (2005)
Pachner move 3 o 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.
Externí odkaz:
https://doaj.org/article/fcbfd65f180845eabe00cc9b7302df25
Autor:
Igor G. Korepanov
This is the second in a series of papers where we construct an invariant of a four-dimensional piecewise linear manifold $M$ with a given middle cohomology class $h\in H^2(M,\mathbb C)$. This invariant is the square root of the torsion of unusual cha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8f51dd5a58fad957563db16a07f7a061