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pro vyhledávání: '"Fock, V."'
Autor:
Fock, V. V.
A.Goncharov and R.Kenyon has defined a class of integrable system on a cluster varieties constructed out of a Newton polygon on the plane. In the present note we show that thiest cluster varieties coincides with the configuration spaces of collection
Externí odkaz:
http://arxiv.org/abs/1503.00289
Autor:
Fock, V. V., Marshakov, A.
We describe a class of integrable systems on Poisson submanifolds of the affine Poisson-Lie groups $\widehat{PGL}(N)$, which can be enumerated by cyclically irreducible elements the co-extended affine Weyl groups $(\widehat{W}\times \widehat{W})^\sha
Externí odkaz:
http://arxiv.org/abs/1401.1606
Autor:
Fock, V. V., Goncharov, A. B.
A positive space is a space with a positive atlas, i.e. a collection of rational coordinate systems with subtraction free transition functions. The set of positive real points of a positive space is well defined. We define a tropical compactification
Externí odkaz:
http://arxiv.org/abs/1104.0407
Autor:
Fock, V. V.
Publikováno v:
Amer. Math. Soc. Transl. Ser.2, 221 (2007)
We show a few propositions in favour of relations between the phase space of 3D gravity, moduli of quasi-Fuchsian groups, global solutions of cosh-Gordon equations and minimal surfaces in hyperbolic spaces.
Externí odkaz:
http://arxiv.org/abs/0811.3356
Autor:
Fock, V. V., Goncharov, A. B.
We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the cluster modular
Externí odkaz:
http://arxiv.org/abs/math/0702397
Autor:
Fock, V. V., Goncharov, A. B.
The main result is a construction, via the quantum dilogarithm, of certain intertwiner operators, which play the crucial role in the quantization of the cluster X-varieties and construction of the corresponding canonical representation.
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Externí odkaz:
http://arxiv.org/abs/math/0702398
Autor:
Fock, V. V., Goncharov, A. B.
We survey explicit coordinate descriptions for two (A and X) versions of Teichmuller and lamination spaces for open 2D surfaces, and extend them to the more general set-up of surfaces with distinguished collections of points on the boundary. Main fea
Externí odkaz:
http://arxiv.org/abs/math/0510312
Autor:
Fock, V. V., Goncharov, A. B.
Starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We describe them as the cluster X-varieties, as defined in math.AG/0311245. In particular they are Poisson varieties. W
Externí odkaz:
http://arxiv.org/abs/math/0508408
Autor:
Fock, V. V., Goncharov, A. B.
We define convex projective structures on 2D surfaces with holes and investigate their moduli space. We prove that this moduli space is canonically identified with the higher Teichmuller space for the group PSL_3 defined in our paper math/0311149. We
Externí odkaz:
http://arxiv.org/abs/math/0405348