In mathematics, a piecewise linear manifold (PL manifold) is a topological manifold together with a piecewise linear structure on it. Such a structure...

piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. A piecewise linear...

which the function is linear Piecewise linear manifold, a topological space formed by gluing together flat spaces Piecewise linear homeomorphism, a topological...

used in a more global sense involving triangulations; see Piecewise linear manifold. Piecewise functions can be defined using the common functional notation...

often generalized: Piecewise linear curve Piecewise polynomial curve, also known as a spline (mathematics) Piecewise linear manifold This disambiguation...

of manifold is a contact manifold. A combinatorial manifold is a kind of manifold which is discretization of a manifold. It usually means a piecewise linear...

Categories of Manifolds Affine manifold Analytic manifold Complex manifold Differentiable (smooth) manifold Piecewise linear manifold Lipschitz manifold Topological...

concerned with when a topological manifold has a piecewise linear structure, and when a piecewise linear manifold has a differential structure. In dimension...

simplicial manifold composed by regular (d − 1)-dimensional simplices and the connection between these slices is made by a piecewise linear manifold of d-simplices...

differentiable manifolds, PL for piecewise linear functions between piecewise linear manifolds, and TOP for continuous functions between topological manifolds. These...

Simplicial continuation, or piecewise linear continuation (Allgower and Georg), is a one-parameter continuation method which is well suited to small to...

manifold. There is no standard usage of this term in mathematics, and so the concept can refer to a triangulation in topology, or a piecewise linear manifold...

in differential topology, a Kervaire manifold K 4 n + 2 {\displaystyle K^{4n+2}} is a piecewise-linear manifold of dimension 4 n + 2 {\displaystyle 4n+2}...

of a piecewise-linear manifold and a topological manifold: a PL structure gives rise to a unique Lipschitz structure. While Lipschitz manifolds are closely...

mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure. Non-simply connected 5-manifolds are impossible...

of replacing a triangulation of a piecewise linear manifold by a different triangulation of a homeomorphic manifold. Pachner moves are also called bistellar...

that a manifold that is a homotopy sphere is a sphere. More precisely, one fixes a category of manifolds: topological (Top), piecewise linear (PL), or...

non-Jordan manifolds. A combinatorial manifold is a kind of manifold which is a discretization of a manifold. It usually means a piecewise linear manifold made...

differentiable manifolds or the category of piecewise-linear manifolds. The notions of irreducibility in algebra and manifold theory are related. An n-manifold is...

smooth manifolds, which are basic in calculus in several variables, mathematical analysis and differential geometry; piecewise-linear manifolds; topological...

distinction between the categories of topological manifolds, differentiable manifolds, and piecewise linear manifolds became apparent. Now consider Alexander's...

a triangulable space. Triangulations can also be used to define a piecewise linear structure for a space, if one exists. Triangulation has various applications...

category of smooth manifolds and smooth functions between them) and PL (the category of piecewise linear manifolds and piecewise linear maps between them)...

homeomorphism f : N → M {\displaystyle f\colon N\to M} of m-dimensional piecewise linear manifolds has an invariant κ ( f ) ∈ H 3 ( M ; Z / 2 Z ) {\displaystyle...

combinatorial manifold is a kind of manifold which is a discretization of a manifold. It usually means a piecewise linear manifold made by simplicial complexes...

In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature...

^{+}(S^{n-1})} provided n ≥ 6 {\displaystyle n\geq 6} . If M is a piecewise linear manifold then the problem of finding the compatible smooth structures on...

point), but not collapsible. Any n-dimensional PL manifold that is collapsible is in fact piecewise-linearly isomorphic to an n-ball. Discrete Morse theory...

Numerical relativity Quantum gravity Euclidean quantum gravity Piecewise linear manifold Euclidean simplex Path integral formulation Lattice gauge theory...

topological 3-manifold has an essentially unique piecewise-linear structure and smooth structure. As corollary, every compact 3-manifold has a Heegaard...