Results 51 to 60 of about 2,939,402 (89)
Grothendieck's Reconstruction Principle and 2-dimensional Topology and Geometry [PDF]
Communications in Contemporary Mathematics, Vol. 1, No. 2 (1999)
125-153, 1999 This paper attempts to relate some ideas of Grothendieck in his Esquisse d'un programme and some of the recent results on 2-dimensional topology and geometry. Especially, we shall discuss the Teichm\"uller theory, the mapping class groups, $SL(2, \bold C)$ representation variety of surface groups, and Thurston's theory of measured laminations.
arxiv
Topology and Geometry for physicists [PDF]
Proceedings of XIII Modave Summer School in Mathematical Physics — PoS(Modave2017), 2018 These lecture notes are based on a series of lectures given in 2017 at the XIII Modave Summer School in Mathematical Physics. These notes are therefore aimed at beginning PhD students in theoretical physics and cover topics in homotopy theory, homology and cohomology, as well as fibre bundles, with applications in condensed matter systems ...
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Unifying Themes in Topological Field Theories [PDF]
arXiv, 2000 We discuss unifying features of topological field theories in 2, 3 and 4 dimensions. This includes relations among enumerative geometry (2d topological field theory) link invariants (3d Chern-Simons theory) and Donaldson invariants (4d topological theory).
arxiv
The topology and geometry of contact structures in dimension three [PDF]
arXiv, 2006 The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
arxiv
Equivariant geometry of Banach spaces and topological groups [PDF]
arXiv, 2016 We study uniform and coarse embeddings between Banach spaces and topological groups. A particular focus is put on equivariant embeddings, i.e., continuous cocycles associated to continuous affine isometric actions of topological groups on separable Banach spaces with varying geometry.
arxiv
Geometry, topology, and string theory [PDF]
, 2003 A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect.
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Toric Topology. Chapter 1: Geometry and combinatorics of polytopes [PDF]
arXiv, 2011 This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
arxiv
Grid Diagrams, Braids, and Contact Geometry [PDF]
Proceedings of Gokova Geometry-Topology Conference 2008, 120--136, 2008 We use grid diagrams to present a unified picture of braids, Legendrian knots, and transverse knots.
arxiv
Geom. Topol. Monogr. 4 (2002) 295-302, 2002 We give a brief survey of abelian torsions of 3-manifolds.
arxiv
Topological aspects of the Dvoretzky Theorem [PDF]
arXiv, 2009 We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.
arxiv