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...

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

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

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...

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

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

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

triangulation describes the replacement of topological spaces by piecewise linear spaces, i.e. the choice of a homeomorphism in a suitable simplicial...

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...

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

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

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

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...

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...

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

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

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}...

such as the category of differentiable manifolds or the category of piecewise-linear manifolds. A 3-manifold is irreducible if and only if it is prime...

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...

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

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

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

^{+}(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...

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

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...

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...

is similar to cobordism, except that one uses piecewise linear or topological instead of smooth manifolds, either oriented or unoriented. The coefficient...

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