相关论文: Topology from the Bottom Up

In this note we study the topology of 3-dimensional initial data sets with horizons of a sort associated with asymptotically locally anti-de Sitter spacetimes. We show that, within this class, those initial data sets which contain no…

The aim of this paper is to provide a gentle introduction to Chabauty topology, while very little background knowledge is assumed. As an example, we provide pictures for the Chabauty space of C*. Note that the description of this space is…

This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…

We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math.

The ad\`eles of a scheme have local components - these are topological higher local fields. The topology plays a large role since Yekutieli showed in 1992 that there can be an abundance of inequivalent topologies on a higher local field and…

This paper tackles the challenging task of 3D visual grounding-locating a specific object in a 3D point cloud scene based on text descriptions. Existing methods fall into two categories: top-down and bottom-up methods. Top-down methods rely…

We develop a simple method of constructing topological spaces from countable posets with finite levels, one which applies to all second countable T_1 compacta. This results in a duality amenable to building such spaces from finite building…

In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.

This is an example on the cohomology of threefolds.

An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.

The note complements topological aspects of the theory of chiral algebras.

This paper has been withdrawn, because its material has been revised and became part of paper math.GT/0010184

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

In this article we survey, and make a few new observations about, the surprising connection between sub-monoids of mapping class groups and interesting geometry and topology in low-dimensions.

Top-down attention plays a crucial role in the human vision system, wherein the brain initially obtains a rough overview of a scene to discover salient cues (i.e., overview first), followed by a more careful finer-grained examination (i.e.,…

[Note to the reader: properties (C2) and (C2)* are under development, in order to form a generalization of (C3) and (C3)*]

We study the topological structure of the quotient of $SU(3)\times SU(3)$ by diagonal conjugation. This is the simplest nontrivial example for the classical reduced configuration space of chromodynamics on a spatial lattice in the…

We study topological properties of the graph topology.

In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.

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.