scholarly journals A spectral triple for noncommutative compact surfaces

2020 ◽  
Vol 120 ◽  
pp. 121-134
Author(s):  
Fredy Díaz García ◽  
Elmar Wagner
Keyword(s):  
Spectral Triple ◽  
Compact Surfaces

scholarly journals Missing the point in noncommutative geometry

Synthese ◽  
2021 ◽  
Author(s):  
Nick Huggett ◽  
Fedele Lizzi ◽  
Tushar Menon
Keyword(s):  
Scalar Field ◽  
Noncommutative Geometry ◽  
Smooth Manifold ◽  
Operational Definition ◽  
Spectral Triple ◽  
Fundamental Quantity

AbstractNoncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes’ spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar field Moyal–Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry.

Unified Approach to Stabilization of Waves on Compact Surfaces by Simultaneous Interior and Boundary Feedbacks of Unrestricted Growth

2013 ◽  
Vol 69 (1) ◽  
pp. 83-122 ◽  
Author(s):  
Marcelo M. Cavalcanti ◽  
Valéria N. Domingos Cavalcanti ◽  
Ryuichi Fukuoka ◽  
Daniel Toundykov
Keyword(s):  
Unified Approach ◽  
Compact Surfaces

scholarly journals Spin-½ Bosonization on Compact Surfaces

1986 ◽  
Vol 57 (7) ◽  
pp. 795-798 ◽  
Author(s):  
J. B. Bost ◽  
Philip Nelson
Keyword(s):  
Compact Surfaces

Quantum Gauge Theory on Compact Surfaces

1993 ◽  
Vol 221 (1) ◽  
pp. 17-52 ◽  
Author(s):  
A. Sengupta
Keyword(s):  
Gauge Theory ◽  
Quantum Gauge Theory ◽  
Compact Surfaces

scholarly journals Quantitative quasisymmetric uniformization of compact surfaces

2017 ◽  
Vol 146 (1) ◽  
pp. 281-293
Author(s):  
Lukas Geyer ◽  
Kevin Wildrick
Keyword(s):  
Compact Surfaces

scholarly journals Generic diffeomorphisms on compact surfaces

2005 ◽  
Vol 187 (2) ◽  
pp. 127-159 ◽  
Author(s):  
Flavio Abdenur ◽  
Christian Bonatti ◽  
Sylvain Crovisier ◽  
Lorenzo J. Díaz
Keyword(s):  
Compact Surfaces
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