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26 relations: Annals of Mathematics, Atlas (topology), Cone (topology), Differentiable manifold, Digital manifold, Digital topology, Exotic sphere, Generalized Poincaré conjecture, H-cobordism, Hauptvermutung, Homology sphere, Homotopy sphere, Isomorphism, Kirby–Siebenmann class, Mathematics, Obstruction theory, PDIFF, Piecewise linear function, Real algebraic geometry, Simplicial complex, Simplicial manifold, Smooth structure, Surgery theory, Suspension (topology), Topological manifold, Triangulation (topology).
Annals of Mathematics
The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.
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Atlas (topology)
In mathematics, particularly topology, one describes a manifold using an atlas.
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Cone (topology)
In topology, especially algebraic topology, the cone CX of a topological space X is the quotient space: of the product of X with the unit interval I.
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Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
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Digital manifold
In mathematics, a digital manifold is a special kind of combinatorial manifold which is defined in digital space i.e. grid cell space.
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Digital topology
Digital topology deals with properties and features of two-dimensional (2D) or three-dimensional (3D) digital images that correspond to topological properties (e.g., connectedness) or topological features (e.g., boundaries) of objects.
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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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Generalized Poincaré conjecture
In the mathematical area of topology, the Generalized Poincaré conjecture is a statement that a manifold which is a homotopy sphere 'is' a sphere.
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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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Hauptvermutung
The Hauptvermutung (German for main conjecture) of geometric topology is the conjecture that any two triangulations of a triangulable space have a common refinement, a single triangulation that is a subdivision of both of them.
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Homology sphere
In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1.
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Homotopy sphere
In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold that is homotopy equivalent to the n-sphere.
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Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
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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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Obstruction theory
In mathematics, obstruction theory is a name given to two different mathematical theories, both of which yield cohomological invariants.
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PDIFF
In geometric topology, PDIFF, for piecewise differentiable, is the category of piecewise-smooth manifolds and piecewise-smooth maps between them.
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Piecewise linear function
In mathematics, a piecewise linear function is a real-valued function defined on the real numbers or a segment thereof, whose graph is composed of straight-line sections.
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Real algebraic geometry
In mathematics, real algebraic geometry is the study of real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomial mappings).
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Simplicial complex
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their ''n''-dimensional counterparts (see illustration).
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Simplicial manifold
In physics, the term simplicial manifold commonly refers to one of several loosely defined objects, commonly appearing in the study of Regge calculus.
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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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Surgery theory
In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by.
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Suspension (topology)
In topology, the suspension SX of a topological space X is the quotient space: of the product of X with the unit interval I.
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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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Triangulation (topology)
In mathematics, topology generalizes the notion of triangulation in a natural way as follows: Triangulation is useful in determining the properties of a topological space.
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PL homeomorphism, PL manifold, PL structure, PL-manifold, PL-structure, Piecewise linear homeomorphism, Piecewise linear structure, Piecewise-linear manifold, Piecewise-linear structure, Piecewise-linear triangulation.
References
[1] https://en.wikipedia.org/wiki/Piecewise_linear_manifold
