Related papers: Periods for topological circle actions
We classify symplectic non-Hamiltonian circle actions on compact connected symplectic 4-manifolds, up to equivariant symplectomorphisms. Namely, we define a set of invariants, show that the set is complete, and determine which values are…
We describe explicit generators for the "real" K-theory of "real" spheres in van Daele's picture. Pulling these generators back along suitable maps from tori to spheres produces a family of Hamiltonians used in the physics literature on…
Placing a Dirac-Schr\"odinger operator along the orbit of a flow on a compact manifold \(M\) defines an \(\R\)-equivariant spectral triple over the algebra of smooth functions on \(M\). We study some of the properties of these triples,…
In this paper, we give Thomae type formula for \KK surfaces $\cS$ given by double covers of the projective plane branching along six lines. This formula gives relations between theta constants on the bounded symmetric domain of type…
The method of topological vertex for topological string theory on toric Calabi-Yau 3-folds is reviewed. Implications of an explicit formula of partition functions in the "on-strip" case, typically the generalized conifolds, are considered.…
This paper establishes new bridges between number theory and modern harmonic analysis, namely between the class of complex functions, which contains zeta functions of arithmetic schemes and closed with respect to product and quotient, and…
On the free loop space of compact symmetric spaces Ziller introduced explicit cycles generating the homology of the free loop space. We use these explicit cycles to compute the string topology coproduct on complex and quaternionic…
In this paper, we study various chaos of topological group or semigroup actions.
Equivalence classes of gapped Hamiltonians compatible with given symmetry constraints, such as those underlying topological insulators, can be defined in many ways. For the non-chiral classes modelled by vector bundles over Brillouin tori,…
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show…
We give indications that outer future trapping horizons play a role in the particular semi-classical instability of an evolving black hole that produces the Hawking's radiation. These are obtained with the use of the Hamilton-Jacobi…
This paper investigates the correlation between $k$-type dynamical properties of $\mathbb{Z}^d$-actions on compact metric spaces and their induced actions on the corresponding hyperspaces. We extend the classical results from discrete…
We propose a toy model for symmetry-breaking or bubbling, in terms of cobordism of manifolds with circle actions free on a possible boundary. The Swan-Tate cohomology $t_\T E$ of a complex-oriented $E_\infty$ ring-spectrum $E$ is the…
In classical mechanics, an action is defined only modulo additive terms which do not modify the equations of motion; in certain cases, these terms are topological quantities. We construct an infinite sequence of higher order topological…
A tautological system, introduced in [16][17], arises as a regular holonomic system of partial differential equations that govern the period integrals of a family of complete intersections in a complex manifold $X$, equipped with a suitable…
We define functionals generalising the Seiberg-Witten functional on closed $spin^c$ manifolds, involving higher order derivatives of the curvature form and spinor field. We then consider their associated gradient flows and, using a gauge…
Consider the Hamiltonian action of a torus on a compact twisted generalized complex manifold $M$. We first observe that Kirwan injectivity and surjectivity hold for ordinary equivariant cohomology in this setting. Then we prove that these…
We study period integrals of CY hypersurfaces in a partial flag variety. We construct a holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can…
The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of…
Let X=H\G be a homogeneous spherical variety for a split reductive group G over the integers o of a p-adic field k, and K=G(o) a hyperspecial maximal compact subgroup of G=G(k). We compute eigenfunctions ("spherical functions") on X=X(k)…