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37 relations: Akbulut cork, Algebraic surface, Casson handle, Ciprian Manolescu, Diffeomorphism, Dolgachev surface, Donaldson's theorem, E8 manifold, Enriques–Kodaira classification, Exotic R4, Exotic sphere, Frank Quinn (mathematician), General relativity, H-cobordism, Homeomorphism, Homotopy, Intersection form (4-manifold), Journal of the American Mathematical Society, K3 surface, Kirby calculus, Kirby–Siebenmann class, Mathematics, Notices of the American Mathematical Society, Piecewise linear manifold, Poincaré conjecture, Presentation of a group, Pseudo-Riemannian manifold, Seiberg–Witten invariants, Simply connected space, Smooth structure, Spacetime, Springer Science+Business Media, Symplectic manifold, Topological manifold, Unimodular lattice, 3-manifold, 5-manifold.
Akbulut cork
In topology, an Akbulut cork is a structure that is frequently used to show that in four dimensions, the smooth h-cobordism theorem fails.
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Algebraic surface
In mathematics, an algebraic surface is an algebraic variety of dimension two.
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Casson handle
In 4-dimensional topology, a branch of mathematics, a Casson handle is a 4-dimensional topological 2-handle constructed by an infinite procedure.
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Ciprian Manolescu
Ciprian Manolescu (born December 24, 1978) is a Romanian-American mathematician, working in gauge theory, symplectic geometry, and low-dimensional topology.
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Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of smooth manifolds.
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Dolgachev surface
In mathematics, Dolgachev surfaces are certain simply connected elliptic surfaces, introduced by.
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Donaldson's theorem
In mathematics, Donaldson's theorem states that a definite intersection form of a simply connected smooth manifold of dimension 4 is diagonalisable.
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E8 manifold
In mathematics, the E8 manifold is the unique compact, simply connected topological 4-manifold with intersection form the ''E''8 lattice.
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Enriques–Kodaira classification
In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes.
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Exotic R4
In mathematics, an exotic R4 is a differentiable manifold that is homeomorphic but not diffeomorphic to the Euclidean space R4.
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Exotic sphere
In differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere.
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Frank Quinn (mathematician)
Frank Stringfellow Quinn, III (born 1946) is an American mathematician and professor of mathematics at Virginia Polytechnic Institute and State University, specializing in geometric topology.
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General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
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H-cobordism
In geometric topology and differential topology, an (n + 1)-dimensional cobordism W between n-dimensional manifolds M and N is an h-cobordism (the h stands for homotopy equivalence) if the inclusion maps are homotopy equivalences.
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Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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Intersection form (4-manifold)
In mathematics, the intersection form of an oriented compact 4-manifold is a special symmetric bilinear form on the 2nd cohomology group of the 4-manifold.
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Journal of the American Mathematical Society
The Journal of the American Mathematical Society (JAMS), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society.
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K3 surface
In mathematics, a K3 surface is a complex or algebraic smooth minimal complete surface that is regular and has trivial canonical bundle.
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Kirby calculus
In mathematics, the Kirby calculus in geometric topology, named after Robion Kirby, is a method for modifying framed links in the 3-sphere using a finite set of moves, the Kirby moves.
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Kirby–Siebenmann class
In mathematics, the Kirby–Siebenmann class is an element of the fourth cohomology group which must vanish if a topological manifold M is to have a piecewise linear structure.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Notices of the American Mathematical Society
Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue.
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Piecewise linear manifold
In mathematics, a piecewise linear (PL) manifold is a topological manifold together with a piecewise linear structure on it.
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Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
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Presentation of a group
In mathematics, one method of defining a group is by a presentation.
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Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.
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Seiberg–Witten invariants
In mathematics, Seiberg–Witten invariants are invariants of compact smooth 4-manifolds introduced by, using the Seiberg–Witten theory studied by during their investigations of Seiberg–Witten gauge theory.
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Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
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Smooth structure
In mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function.
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Spacetime
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form.
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Topological manifold
In topology, a branch of mathematics, a topological manifold is a topological space (which may also be a separated space) which locally resembles real n-dimensional space in a sense defined below.
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Unimodular lattice
In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1.
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3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.
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5-manifold
In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.
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11/8 conjecture, 4 manifold, 4-manifolds, Four-manifold.
References
[1] https://en.wikipedia.org/wiki/4-manifold
