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pro vyhledávání: '"53D05"'
Hypersemitoric systems are a class of integrable systems on $4$-dimensional symplectic manifolds which only have mildly degenerate singularities and where one of the integrals induces an effective Hamiltonian $S^1$-action and is proper. We introduce
Externí odkaz:
http://arxiv.org/abs/2411.17509
We develop the concept of a homogeneity supermanifold, which is more general than most of the approaches to graded manifolds present in the literature. Instead of doing it via ringed spaces and sheaves of graded algebras, we prefer a purely different
Externí odkaz:
http://arxiv.org/abs/2411.00537
Autor:
Wagner, Maxime, Wurzbacher, Tilmann
We show the equivalence of different conditions on a classical field psi to be a solution of the field equations, notably in terms of the Hamilton-Volterra equations, the principle of least action and several conditions based on the contraction of th
Externí odkaz:
http://arxiv.org/abs/2410.21068
Autor:
Sugimoto, Yoshihiro
In this paper, we study homological monodromy of a Lagrangian submanifold. First, we show that homological Lagrangian monodromy is trivial if Hofer energy of a Hamiltonian isotopy is smaller than the minimum energy of J-holomorphic spheres and discs.
Externí odkaz:
http://arxiv.org/abs/2410.20677
Autor:
Ritter, Alexander F., Živanović, Filip
We prove that Floer theory induces a filtration by ideals on equivariant quantum cohomology of symplectic manifolds equipped with a $\mathbb{C}^*$-action. In particular, this gives rise to Hilbert-Poincar\'e polynomials on ordinary cohomology that de
Externí odkaz:
http://arxiv.org/abs/2410.17237
Autor:
Kim, Hyunmoon
We develop a correspondence between the orbits of the group of linear symplectomorphisms of a real finite dimensional symplectic vector space in the complex Lagrangian Grassmannian and the Grassmannians of linear subspaces of the real symplectic vect
Externí odkaz:
http://arxiv.org/abs/2410.16869
We propose a simple definition of a Born geometry in the framework of K\"unneth geometry. While superficially different, this new definition is equivalent to the known definitions in terms of para-quaternionic or generalized geometries. We discuss in
Externí odkaz:
http://arxiv.org/abs/2410.15402
Autor:
Bonciocat, Ciprian Mircea
In 1995, Cohen, Jones and Segal proposed a method of upgrading any given Floer homology to a stable homotopy-valued invariant. For a generic pseudo-gradient Morse-Bott flow on a closed smooth manifold $M$, we rigorously construct the conjectural stab
Externí odkaz:
http://arxiv.org/abs/2409.11278
While the construction of symplectic integrators for Hamiltonian dynamics is well understood, an analogous general theory for Poisson integrators is still lacking. The main challenge lies in overcoming the singular and non-linear geometric behavior o
Externí odkaz:
http://arxiv.org/abs/2409.04342
Autor:
Guggisberg, Yann, Ziltener, Fabian
We call a metric space $s$-negligible iff its $s$-dimensional Hausdorff measure vanishes. We show that every countably $m$-rectifiable subset of $\mathbb{R}^{2n}$ can be displaced from every $(2n-m)$-negligible subset by a Hamiltonian diffeomorphism
Externí odkaz:
http://arxiv.org/abs/2408.17444