Related papers: Some remarks on cosymplectic 3-structures
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
We introduce the Kodaira dimension of contact 3-manifolds and establish some basic properties. In particular, contact 3-manifolds with distinct Kodaria dimensions behave differently when it comes to the geography of various kinds of…
We study the monopole h-invariants of 3-manifolds from a topological perspective based on Lidman and Manolescu's description of monopole Floer homology in terms of Seiberg-Witten-Floer homotopy types. We investigate the possible dependence…
A brief survey of real algebraic structures on topological spaces is given. This article is written for the Gokova Gemetry/Topology Conference proceedings.
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…
In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds…
Basic properties of even (odd) supermanifolds endowed with a connection respecting a given symplectic structure are studied. Such supermanifolds can be considered as generalization of Fedosov manifolds to the supersymmetric case.
This short survey article reviews current understand- ing of the structure of noetherian Hopf algebras. The focus is on homological properties. A number of open problems are listed.
We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of…
Let $X$ be surface with isolated singularities in the complex projective space $P^3$ and let denote $Y$ the smooth part of $X$. In this note we discuss some aspects of the topology of such quasi-projective surfaces $Y$: the fundamental…
We construct orbifolds with quasitoric boundary and show that they have stable almost complex structure. We show that a quasitoric orbifold is complex cobordant to finite disjoint copies of complex orbifold projective spaces. Finally some…
In this paper we determine the topology of three-dimensional complete orientable Riemannian manifolds with a uniform lower bound of sectional curvature whose volume is sufficiently small.
This text introduces geometric quantization on orbifolds. After reviewing the necessary background, it develops new treatments of prequantization, polarizations, and metaplectic correction for symplectic orbifolds.
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.
We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build…
In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The…
Recent results concerning the relation of topology and low-lying fermion modes are summarized.
We survey the properties of Brody and Kobayashi hyperbolic manifolds.
The topological classification of gradient like Morse-Smale vector fields and diffeomorphisms on 3-manifolds was obtained.