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...

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

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

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

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

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

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...

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

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

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...

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

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...

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

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...

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

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...

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

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}...

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

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...

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

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

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

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...

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...

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

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

On the other hand, some authors replace "piecewise linear" with "piecewise quadratic" or even "piecewise polynomial". The author might then say "higher...

problems is already known to be intractable. For manifolds of dimension at most 6, any piecewise linear (PL) structure can be smoothed in an essentially...