All posts under category "Mathematics / Math.SG"
Suppose that f:V->W is an embedding of closed oriented manifolds whose normal bundle has the structure of a complex vector bundle. It is well known in both complex and symplectic geometry that one can then construct a manifold W' which is the blow-up of W along V. Assume that dim(W)>2.dim(V)+2 and t
We investigate the detailed dynamics of multidimensional Hamiltonian systems by studying the evolution of volume elements formed by unit deviation vectors about their orbits. The behavior of these volumes is strongly influenced by the regular or chaotic nature of the motion, the number of deviation
We prove that an arbitrary Poisson structure omega^{ij}(u) and an arbitrary closed 3-form T_{ijk}(u) generate the local Poisson structure A^{ij}(u,u_x) = M^i_s(u,u_x)omega^{sj}(u), where M^i_s(u,u_x)(delta^s_j + omega^{sp}(u)T_{pjk}(u)u^k_x) = delta^i_j, on the corresponding loop space. We obtain al
Let $G$ be a finite group and $Y$ a $G$-gerbe over an orbifold $B$. A disconnected orbifold $hat{Y}$ and a flat U(1)-gerbe $c$ on $hat{Y}$ is canonically constructed from $Y$. Motivated by a proposal in physics, we study a mathematical duality between the geometry of the $G$-gerbe $Y$ and the geomet
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