相关论文: Topology and physics-a historical essay

This is a philosophy paper rather than mathematical physics work. I will publish it in some other place.

In three articles published in CNJ in 2012 and 2016 , we discussed some links between mathematical sciences, coin minting and numismatics. This article is a continuation of this cycle. It tells the story of selected important developments…

This is a series of lecture notes explaining topos theory and its application in physics.

We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth of the latter theory and its evolution in the…

In a recent preprint, we discussed geometric lifts, and in particular the notion of St\"ackel lift. In this note, we wish to clarify several aspects raised in the comment arXiv:2511.05765.

This historical introduction is in two parts. The first is reprinted with permission from ``A century of mathematics in America, Part II,'' Hist. Math., 2, Amer. Math. Soc., 1989, pp.543-585. Virtually no change has been made to the…

Econophysics is a new area developed recently by the cooperation between economists, mathematicians and physicists. It's not a tool to predict future prices of stocks and exchange rates. It applies idea, method and models in Statistical…

We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…

This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.

This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.

The parts contributed by the author in recent discussions with several physicists and mathematicians are reviewed, as they have been occasioned by the 2006 book "The Trouble with Physics", of Lee Smolin. Some of the issues addressed are the…

The earlier history of two--photon physics is reviewed.

In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…

This article is a short nontechnical survey of recent progresses in fluid dynamics and differential geometry, relating a conjecture of Lars Onsager to the work of Nash on isometric embeddings.

Topos theory occupies a singular place in contemporary mathematics: born from Grothendieck's algebraic geometry, it has emerged as a unifying language for geometry, topology, algebra, and logic. This book offers a progressive introduction…

This expository essay is aimed at introducing the Jones polynomial. We will see the encapsulation of the Jones polynomial, which will involve topics in functional analysis and geometrical topology; making this essay an interdisciplinary…

This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi…

This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…

The present discussion concerning certain fundamental physical theories (such as string theory and multiverse cosmology) has reopened the demarcation problem between science and non-science. While parts of the physics community see the…

The tight versus overtwisted dichotomy has been an essential organizing principle and driving force in 3-dimensional contact geometry since its inception around 1990. In this article, we will discuss the genesis of this dichotomy in…