Results 1 to 10 of about 178 (121)
Noncommutative topology and the world’s simplest index theorem [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2010 In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a
Erik Van Erp
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From factorizations of noncommutative polynomials to combinatorial topology [PDF]
Open Mathematics, 2010 Abstract This is an extended version of a talk given by the author at the conference “Algebra and Topology in Interaction” on the occasion of the 70th Anniversary of D.B. Fuchs at UC Davis in September 2009. It is a brief survey of an area originated around 1995 by I. Gelfand and the speaker.
Retakh Vladimir
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An essay on noncommutative topology
Topology and Its Applications, 1989 By ``noncommutative topology'' the authors mean \textit{C. J. Mulvey}'s theory of quantales [Rend. Circ. Mat. Palermo., II. Ser., Suppl. 12, 99- 104 (1986; Zbl 0633.46065)]. This was originally introduced in the hope of providing a ``Gelfand-type'' representation for noncommutative \(C^*\)-algebras.
Francis Borceux
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A noncommutative view on topology and order
Journal of Geometry and Physics, 2009 31 pages.
Fabien Besnard
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Noncommutative geometry, topology, and the standard model vacuum [PDF]
Journal of Mathematical Physics, 2006 As a ramification of a motivational discussion for previous joint work, in which equations of motion for the finite spectral action of the standard model were derived, we provide a new analysis of the results of the calculations therein, switching from the perspective of spectral triple to that of Fredholm module and thus from the analogy with ...
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The noncommutative topology of anti-self-dual gauge fields
Journal of Geometry and Physics, 2013 25 pages, no figures; v2 typos corrected, refs ...
Simon Brain
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A noncommutative geometric analysis of a sphere–torus topology change [PDF]
Journal of Geometry and Physics, 2004 18 pages. 16 small eps figures.
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Noncommutative tensor triangulated categories and coherent frames
Comptes Rendus. Mathématique, 2023 We develop a point-free approach for constructing the Nakano–Vashaw–Yakimov–Balmer spectrum of a noncommutative tensor triangulated category under certain assumptions.
Mallick, Vivek Mohan, Ray, Samarpita
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Noncommuting Momenta of Topological Solitons [PDF]
Physical Review Letters, 2014 5 +1 pages, including Supplemental Material; v4: new references added, published ...
Watanabe, Haruki, Murayama, Hitoshi
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Structure Sheaves and Noncommutative Topologies [PDF]
Journal of Algebra, 1997 The main purpose of this paper is to construct structure sheaves over noncommutative topologies associated to an arbitrary left noetherian ring. In the first section the authors quickly recollect some of the main notions, constructions and results, which will be needed throughout.
Garcia, M. +2 more
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