?
Сборник научно- исследовательских работ студентов — победителей Конкурса НИРС
The goal of this thesis is to understand symplectic mapping class group of rational 4-manifolds and how it changes, when the cohomology class of the symplectic form varies. For this aims, we will show that in some cases this group admits a realization as the fundamental group of the complement to certain divisor on Hilbert scheme of points on СP2. This divisor is the locus of special constellations of points which parameterize rational complex surfaces X with rational (-2)-curves on X. In the paper we will describe irreducible components of this divisor and show that the loops around the components of the divisor are natural generators of the symplectic mapping class group.
Language:
English
Keywords: Symplectic Geometry
V. Gorbounov, Guterman L., Bychkov B. et al., Journal of Geometry and Physics 2025 Vol. 207 P. 0
In this paper we relate a well-known in symplectic geometry compactification of the space of symmetric bilinear forms considered as a chart of the Lagrangian Grassmannian to the specific compactifications of the space of electrical networks in the disc obtained in \cite{L}, \cite{CGS} and \cite{BGKT}. In particular, we state an explicit connection between these works ...
Added: October 4, 2024
Lekili Y., Polishchuk A., Compositio Mathematica 2020 Vol. 156 No. 7 P. 1310–1347
Using Auroux's description of Fukaya categories of symmetric products of punctured surfaces, we compute the partially wrapped Fukaya category of the complement of k+1 generic hyperplanes in ℂℙ^n, for k≥n, with respect to certain stops in terms of the endomorphism algebra of a generating set of objects. The stops are chosen so that the resulting algebra is formal. In ...
Added: August 12, 2020
Alekseeva D., Shevchishin V., , in: Сборник научно-исследовательских работ по итогам конкурса НИРС НИУ ВШЭ – 2016.: [б.и.], 2017. P. 171–200.
The goal of this diploma thesis is to understand symplectic mapping class group of rational 4-manifolds and how it changes, when the cohomology class of the symplectic form varies. For this aims, we will show that in some cases this group admits a realization as the fundamental group of the complement to certain divisor on ...
Added: April 20, 2020
Pushkar P. E., / Series arXiv "math". 2016. No. arXiv:1602.07948.
We construct counterexamples to lifting properties of Hamiltonian and contact isotopies ...
Added: December 7, 2016
Pushkar P. E., / Series arXiv "math". 2016. No. arXiv:1602.08743.
We prove a Chekanov-type theorem for the spherization of the cotangent bundle ST∗B of a closed manifold B. It claims that for Legendrian submanifolds in ST∗B the property "to be given by a generating family quadratic at infinity" persists under Legendrian isotopies. ...
Added: December 7, 2016
Bondal A. I., Zhdanovskiy I., , in: Primitive Forms and Related Subjects — Kavli IPMU 2014.: Tokyo: Mathematical Society of Japan, 2019. P. 1–18.
The goal of these notes is to show that the classification problem of algebraically unbiased system of projectors has an interpretation in symplectic geometry. This leads us to a description of the moduli space of algebraically unbiased bases as critical points of a potential functions, which is a Laurent polynomial in suitable coordinates. The Newton ...
Added: October 22, 2015
Entov M., Verbitsky M., / Series math "arxiv.org". 2014.
Let M be a closed symplectic manifold of volume V. We say that M admits a full symplectic packing by balls if any collection of symplectic balls of total volume less than V admits a symplectic embedding to M. In 1994 McDuff and Polterovich proved that symplectic packings of Kahler manifolds can be characterized in ...
Added: February 5, 2015
Galkin S., Golyshev V., Iritani H., Duke Mathematical Journal 2016 Vol. 165 No. 11 P. 2005–2077
We propose Gamma Conjectures for Fano manifolds which can be thought of as a square root of the index theorem. Studying the exponential asymptotics of solutions to the quantum differential equation, we associate a principal asymptotic class A_F to a Fano manifold F. We say that F satisfies Gamma Conjecture I if A_F equals the ...
Added: November 18, 2014
Galkin S., Golyshev V., Iritani H., / Series math "arxiv.org". 2014. No. 1404.6407.
We propose Gamma Conjectures for Fano manifolds which can be thought of as a square root of the index theorem. Studying the exponential asymptotics of solutions to the quantum differential equation, we associate a principal asymptotic class A_F to a Fano manifold F. We say that F satisfies Gamma Conjecture I if A_F equals the ...
Added: May 4, 2014
Abouzaid M., Auroux D., Efimov Alexander I. et al., Journal of the American Mathematical Society 2013 Vol. 26 No. 4 P. 1051–1083
We prove that the wrapped Fukaya category of a punctured sphere ($ S^{2}$ with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror Landau-Ginzburg model, proving one side of the homological mirror symmetry conjecture in this case. By investigating fractional gradings on these categories, we conclude that ...
Added: October 31, 2013
Vsevolod Shevchishin, / Series math "arxiv.org". 2010.
We introduce the secondary Stiefel-Whitney class $\tilde w_2$ of homotopically trivial diffeomorphisms and show that a homotopically trivial symplectomorphism of a ruled 4-manifold is isotopic to identity if and only if the class $\tilde w_2$ vanishes.
Using this, we give a detailed description of the combinatorial structure of the diffeotopy group of ruled symplectic 4-manifolds ...
Added: March 18, 2013
V. V. Shevchishin, Izvestiya. Mathematics 2009 Vol. 73 No. 4 P. 797–859
In this paper we prove the non-existence of Lagrangian embeddings of the Klein bottle K in R4 and CP2. We exploit the existence of a special embedding of K in a symplectic Lefschetz pencil pr:X→S2 and study its monodromy. As the main technical tool, we develop the combinatorial theory of mapping class groups. The results ...
Added: March 18, 2013
Slavnov S. A., Theoretical Computer Science 2006 Vol. 357 No. 1-3 P. 215–229
Added: March 4, 2013
Slavnov S. A., Annals of Pure and Applied Logic 2005 Vol. 131 No. 1-3 P. 177–225
Added: March 4, 2013
Springer, 2013.
Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry. ...
Added: February 20, 2013
Verbitsky M., Communications in Mathematical Physics 2013 Vol. 324 No. 1 P. 173–177
Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kahler manifold. We prove that any connected component of the moduli space of pseudoholomorphic curves on M is compact. This can be used to study pseudoholomorphic curves on a ...
Added: February 16, 2013