相关论文: Non-simply connected symplectic fillings of lens s…

We construct a positive allowable Lefschetz fibration over the disk on any minimal weak symplectic filling of the canonical contact structure on a lens space. Using this construction we prove that any minimal symplectic filling of the…

The list of properties of Fibonacci numbers F(n) (with multifaceted relevance in physics) is complemented by an empirical observation that in combination with the "next" family of the "delayed Fibonacci" numbers G(n) called, for…

Let (m,b) a pair of natural numbers. For m even (resp. m odd and b greater than or equal to 2) we show that if there is an m-dimensional non-formal compact oriented manifold whose first Betti number equals b, there is also a symplectic…

This paper considers the problem of determining the smallest (as measured by the second Betti number) smooth negative-definite filling of a lens space. The main result is to classify those lens spaces for which the associated…

We describe all abelian groups which can appear as the fundamental groups of closed symplectically aspherical manifolds. The proofs use the theory of symplectic Lefschetz fibrations.

We complete the classification of symplectic fillings of tight contact structures on lens spaces. In particular, we show that any symplectic filling $X$ of a virtually overtwisted contact structure on $L(p,q)$ has another symplectic…

The main result is a general approximation theorem for normalised Betti numbers for Farber sequences of lattices in totally disconnected groups. Further, we contribute some computations and complements to the general theory of $L^2$-Betti…

We show that the set of the numbers that are the sum of a prime and a Fibonacci number has positive lower asymptotic density.

In this short note, we make an observation relating symplectic packings of the standard symplectic ball by two sets and Hamiltonian linking.

We prove that adjoint orbits of semisimple Lie algebras have the structure of symplectic Lefschetz fibrations. We then describe the topology of the regular and singular fibres, in particular calculating their middle Betti numbers. For the…

We obtain the symplectic group as an amalgam of low rank subgroups akin to Levi components. We do this by having the group act flag-transitively on a new type of geometry and applying Tits' lemma. This provides a new way of recognizing the…

We study some symplectic geometric aspects of rationally connected 4-folds. As a corollary, we prove that any smooth projective 4-fold symplectic deformation equivalent to a Fano 4-fold of pseudo-index at least 2 or a rationally connected…

Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame theory and show that many important classes of frames have…

We prove that every compact complex surface with odd first Betti number admits a locally conformally symplectic $2$-form which tames the underlying almost complex structure.

We prove that the thin parts of arithmetically defined locally symmetric space take up a negligible part of their volume and deduce asymptotic results on their Betti numbers.

At this paper, we derive some relationships between permanents of one type of lower-Hessenberg matrix and the Fibonacci and Lucas numbers and their sums.

In this paper we characterize the definiteness of the discrete symplectic system, study a nonhomogeneous discrete symplectic system, and introduce the minimal and maximal linear relations associated with these systems. Fundamental…

In the first part of the paper we present a classification of fake lens spaces of dimension >= 5 whose fundamental group is the cyclic group of order N >= 2. The classification uses and extends the results of Wall and others in the case N =…

This is a continuation of an earlier preprint (math.GT/0209121) under the same title. These papers grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or…

In a paper by Lin an interesting family of semipermutations comes out to index the elements of a cohomology basis of a Hessenberg type variety. The corresponding Betti numbers are a generalization of Eulerian numbers. We show three…