We consider symplectic fibrations as in Guillemin-Lerman-Sternberg, and derive a spectral sequence to compute the Floer cohomology of certain fibered Lagrangians sitting inside compact fibration with small monotone fibers rational base. show if field coefficients fiber Lagrangian vanishes, then total also vanishes. give an application non-torus Gelfand-Cetlin system Flag manifolds, that their

of the Dissertation Applications of the Seiberg-Witten equations to the Differential Geometry of non-compact Kähler manifolds by Ilya Elson Doctor of Philosophy in Mathematics Stony Brook University 2014 Soon after the introduction of the Seiberg-Witten equations, and their magnificent application to the differential topology of 4manifolds, LeBrun [LeB95a] used these equations to study differen...

We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed geodesics. This result generalizes the classical theorem of Duistermaat-Guillemin for compact manifolds and the results of GuillopéZworski, Perry, and Guillarmou-Naud...

In this note we introduce a Yang-Mills bar equation on complex vector bundles E provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on E can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of...

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be Kähler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable tangent bundle (with respect to some Gauduchon metric on it) are locally homogeneous. In particular, if the geometric structure is rigid in Gromov’s sense, then the ...

Model theory is a branch of mathematical logic whose techniques have proven to be useful in several disciplines, including algebra, algebraic geometry and number theory. The last fifteen years have also seen the application of model theory to bimeromorphic geometry, which is the study of compact complex manifolds up to bimeromorphic equivalence. In this article I will try to explain why logic s...

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius condition for spheres. For this aim we first describe the manifold with some pa...

A manifold with a “Lie structure at infinity” is a non-compact manifold M0 whose geometry is described by a compactification to a manifold with corners M and a Lie algebra V of vector fields on M subject to constraints only on M rM0. This definition recovers several classes of non-compact manifolds that were studied before: manifolds with cylindrical ends, manifolds that are Euclidean at infini...

We show that the theory of stable complex G-cobordisms, for a torus G, is embedded into the theory of stable complex G-cobordisms of not necessarily compact manifolds equipped with proper abstract moment maps. Thus the introduction of such non-compact cobordisms in the stable complex G-cobordism theory does not lead to new relations. 1. Proper abstract moment maps. The main objective of this pa...

Studied are moduli spaces of self dual or anti-self dual connections on noncommutative 4-manifolds, especially deformation quantization of compact spin Riemannian 4-manifolds and their isometry groups have 2-torus subgroup. Then such moduli spaces of irreducible modules associated with highestweights of compact connected semisimple Lie groups are smooth manifolds with dimension determined by th...