Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAbelian Analytic Torsion and Symplectic Volume
108
0
0.0
(
0
)
Authors
Brendan McLellan
Ask ChatGPT about the research
No Arabic abstract
This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections. This identification computes the analytic torsion explicitly in terms of Seifert data.
rate research
Read More
For some geometries including symplectic and contact structures on an n-dimensional manifold, we introduce a two-step approach to Gromovs h-principle. From formal geometric data, the first step builds a transversely geometric Haefliger structure of codimension n. This step works on all manifolds, even closed. The second step, which works only on open manifolds and for all geometries, regularizes the intermediate Haefliger structure and produces a genuine geometric structure. Both steps admit relative parametri
Let $f$ be the gluing map of a Heegaard splitting of a 3-manifold $W$. The goal of this paper is to determine the information about $W$ contained in the image of $f$ under the symplectic representation of the mapping class group. We prove three main results. First, we show that the first homology group of the three manifold together with Seiferts linking form provides a complete set of stable invariants. Second, we give a complete, computable set of invariants for these linking forms. Third, we show that a slight augmentation of Birmans determinantal invariant for a Heegaard splitting gives a complete set of unstable invariants.
In this paper, we study strong symplectic fillability and Stein fillability of some tight contact structures on negative parabolic and negative hyperbolic torus bundles over the circle. For the universally tight contact structure with twisting $pi$ in $S^1$-direction on a negative parabolic torus bundle, we completely determine its strong symplectic fillability and Stein fillability. For the universally tight contact structure with twisting $pi$ in $S^1$-direction on a negative hyperbolic torus bundle, we give a necessary condition for it being strongly symplectically fillable. For the virtually overtwisted tight contact structure on the negative parabolic torus bundle with monodromy $-T^n$ ($n<0$), we prove that it is Stein fillable. By the way, we give a partial answer to a conjecture of Golla and Lisca.
In this article we define the analytic torsion of finite volume orbifolds $Gamma backslash mathbb{H}^{2n+1}$ and study its asymptotic behavior with respect to certain rays of representations.
We apply Menkes JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving diffeomorphism of strong symplectic fillings of lens spaces. We show that fillings of contact manifolds obtained by surgery on certain Legendrian negative cables are the result of attaching a symplectic 2-handle to a filling of a lens space. For large families of contact structures on Seifert fibered spaces over $S^2$, we reduce the problem of classifying symplectic fillings to the same problem for universally tight or canonical contact structures. Finally, virtually overtwisted circle bundles over surfaces with genus greater than one and negative twisting number are seen to have unique exact fillings.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
