Results 1 to 10 of about 235,700 (154)

Classical Poincaré Conjecture via 4D Topology [PDF]

Journal of Mathematical Techniques and Computational Mathematics, 2021
The classical Poincaré conjecture that every homotopy 3-sphere is diffeomorphic to the 3-sphere is confirmed by Perelman in arXiv papers solving Thurston’s program on geometrizations of 3-manifolds.
Akio Kawauchi
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Differentiations of Nonlinear Functions Related to States in Magic(n), Cosmology and the Poincare Conjecture

Journal of Human, Earth, and Future, 2020
Results for area differentiations and potential differentiations are related to concepts in cosmology, and to magic(n). The shapes of a sphere and other geometries will be discussed for 3 and higher dimensions and the Poincare conjecture is interpreted ...
Lena J-T Strömberg
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Negation of the Smooth Poincare Conjecture in Dimension 4 and Negation of the Tsirelson’s Conjecture Shed Light on Quantum Gravity

Universe
If spacetime is a physical object, it is conceivable that it loses its integrity or is destroyed in some way as a continuum in an abrupt process initiated in spacetime itself.
Jerzy Król, Torsten Asselmeyer-Maluga
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Recent progress on the Poincaré conjecture and the classification of 3-manifolds [PDF]

, 2004
If M is a closed 3-manifold with trivial fundamental group, then is M diffeomorphic to S? The Poincare Conjecture is that the answer to this question is “Yes.” Developing tools to attack this problem formed the basis for much of the work in 3-dimensional
John Morgan
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Exploring Non-orientable Topology: Deriving the Poincaré Conjecture and Possibility of Experimental Vindication With Liquid Crystal

Social Science Research Network
This review investigates the potential of non-orientable topology as a fundamental framework for understanding the Poincaré conjecture and its implications across various scientific disciplines.
Victor Christianto, Florentín Smarandache   +1 more
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Man and machine thinking about the smooth 4-dimensional Poincaré conjecture [PDF]

, 2010
While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincare conjecture (SPC4) for over 30 years, until recently no invariant has existed which could potentially distinguish these examples from the standard 4 ...
Michael Freedman, Robert E. Gompf, Scott Morrison, Kevin Walker   +3 more
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The Baum-Connes conjecture, noncommutative Poincaré duality, and the boundary of the free group [PDF]

International Journal of Mathematics and Mathematical Sciences, 2003
Heath Emerson
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The generalized Poincaré conjecture in higher dimensions [PDF]

, 1960
The Poincaré conjecture says that every simply connected closed 3-manifold is homeomorphic to the 3-sphere S. This has never been proved or disproved. The problem of showing whether every closed simply connected w-manifold which has the homology groups ...
Stephen T. Smale
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Rigor with Machine Learning from Field Theory to the Poincaré Conjecture [PDF]

Nature Reviews Physics
Despite their successes, machine learning techniques are often stochastic, error-prone and blackbox. How could they then be used in fields such as theoretical physics and pure mathematics for which error-free results and deep understanding are a must? In
Sergei Gukov, James Halverson, Fabian Ruehle   +2 more
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Poincaré conjecture: Aproblem solved after a century of new ideas and continuedwork

, 2017
The Poincare conjecture is a topological problem established in 1904 by the French mathematician Henri Poincare. It characterises three-dimensional spheres in a very simple way.
María Teresa Lozano Imìzcoz
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