相关论文: Problems on homology manifolds

This paper gives a detailed construction of Seiberg-Witten-Floer homology for a closed oriented 3-manifold with a non-torsion $\spinc$ structure. Gluing formulae for certain 4-dimensional manifolds splitting along an embedded 3-manifold are…

In this paper we develop a theory for constructing an invariant of closed oriented 3-manifolds, given a certain type of Hopf algebra. Examples are given by a quantised enveloping algebra of a semisimple Lie algebra, or by a semisimple…

An abstract construction of coarse spaces for non-Hermitian problems and non-Hermitian domain decomposition preconditioners based on extended generalized eigenproblems was proposed in [Nataf and Parolin, arXiv:2404.02758] and analyzed on…

This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.

Since its beginnings, every Cycles and Colourings workshop holds one or two open problem sessions; this document contains the problems (together with notes regarding the current state of the art and related bibliography) presented by…

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…

The Directed Oberwolfach Problem can be considered as the directed version of the well-known Oberwolfach Problem, first mentioned by Ringel at a conference in Oberwolfach, Germany in 1967. In this paper, we describe some new partial results…

These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.

We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.

Report of the Higgs Working Group to appear in the Proceedings of the Workshop "Physics with $\ee$ Linear Colliders", Annecy-Gran Sasso-Hamburg, Feb. 4 - Sept. 1, 1995, P.M. Zerwas (editor).

The article contains a few questions and speculations related to the moduli spaces of curves, K3 surfaces, maps, and sheaves presented in the problem session of the AGNES conference in Amherst (April 2010).

This re-certifying paper describes the details of the Morse homology of manifolds with boundary, introduced by the author before, in terms of handlebody decompositions.

The 11th workshop, Descriptional Complexity of Formal Systems 2009, is taking place in Magdeburg, Germany, on July 6-9, 2009. It is jointly organized by the IFIP Working Group 1.2 on Descriptional Complexity and by the Faculty of Computer…

We calculate the cohomology rings of a collection of seven dimensional manifolds supporting an S^3 x S^3-action with one dimensional orbit space. These manifolds are of interest to differential geometers studying non-negative and positive…

These are the mini-proceedings of the workshop ``Spontaneously Broken Chiral Symmetry and Hard QCD Phenomena" held at the Physikzentrum Bad Honnef from July 15 to 19, 2002. Every author presents a summary of his talk. The transparencies of…

This is not a research article. This is a partial version of a mini-cours which I gave at a meeting of the ACI Jeunes Chercheurs "Dynamique des applications polynomiales" in Toulouse in november 2004. This text includes two parts of that…

Often, high dimensional data lie close to a low-dimensional submanifold and it is of interest to understand the geometry of these submanifolds. The homology groups of a manifold are important topological invariants that provide an algebraic…

The classification of even-homogeneous complex supermanifolds of dimension 1|m, m\leq 3, on CP^1 up to isomorphism is given. An explicit description of such supermanifolds in terms of local charts and coordinates is obtained.

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

This is the extended abstract of the talk given at the workshop "Geometry and physics of Higgs bundles", held at the Mathematisches Forschungsinstitut Oberwolfach in May 2019.