相关论文: Contact structures and periodic fundamental groups

Contact manifolds are odd-dimensional smooth manifolds endowed with a maximally non-integrable field of hyperplanes. They are intimately related to symplectic manifolds, i.e. even-dimensional smooth manifolds endowed with a closed…

Periodic surface homemorphisms (diffeomorphisms) play a significant role in the the Nielsen-Thurston classification of surface homeomorphisms. Periodic surface homeomorphisms can be described (up to conjugacy) by using data sets which are…

Using standard results from higher (secondary) index theory, we prove that the positive scalar curvature bordism groups of a cartesian product GxZ are infinite in dimension 4n if n>0 G a group with non-trivial torsion. We construct…

A $b$-contact structure on a $b$-manifold $(M,Z)$ is a Jacobi structure on $M$ satisfying a transversality condition along the hypersurface $Z$. We show that, in three dimensions, $b$-contact structures with overtwisted three-dimensional…

We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic…

We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the…

In this paper we study the topology of compact manifolds of positive isotropic curvature (PIC). There are many examples of non-simply connected compact manifolds with positive isotropic curvature. We prove that the fundamental group of a…

In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex…

We introduce a new geometric structure on differentiable manifolds. A \textit{Contact} \textit{Pair}on a manifold $M$ is a pair $(\alpha,\eta) $ of Pfaffian forms of constant classes $2k+1$ and $2h+1$ respectively such that $\alpha\wedge…

We prove the existence of essential loops in the space of contact structures on torus bundles over the circle.

In all odd dimensions $\geq 5$ we produce examples of manifolds admitting pairs of Sasaki structures with different basic Hodge numbers. In dimension $5$ we prove more precise results, for example we show that on connected sums of copies of…

Let $M$ be a three-dimensional contact manifold and $\psi:D\setminus\{0\}\to M\times{\Bbb R}$ a finite-energy pseudoholomorphic map from a punctured disc in ${\Bbb C}$, that is asymptotic to a periodic orbit of the Reeb vector field. This…

We show that two properly embedded compact surfaces in an orientable 4-manifold are cobordant if and only if they are $\mathbb{Z}/2$-homologous and either the 4-manifold has boundary or the surfaces have the same normal Euler number. If the…

Let $\pi$ be a group satisfying the Farrell-Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincar\'e duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$…

In the spirit of Sullivan's paper "Cycles for the Dynamical Study of Foliated Manifolds and Complex Manifolds", existence of a contact structure on a closed manifold $M$ is shown to be equivalent to existence of an ample $S^1$-invariant…

We prove that the stable moduli space of $(n-1)$-connected, $n$-parallelizable, $(2n+1)$-dimensional manifolds is homology equivalent to an infinite loopspace for $n \geq 4, n \neq 7$. The main novel ingredient is a version of the cobordism…

We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the…

We show, up to h-cobordism, that the existence and uniqueness of connected sum decompositions of oriented 4-dimensional manifolds is an invariant of homotopy equivalence, assuming that the fundamental group of each summand is "good" in the…

For a compact contact manifold it is shown that the anisotropic Folland-Stein function spaces form an algebra. The notion of anisotropic regularity is extended to define the space of Folland-Stein contact diffeomorphisms, which is shown to…

We survey some recent results concerning the behaviour of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.