nLab piecewise-linear manifold

Redirected from "PL manifold".
Note: piecewise-linear manifold and piecewise-linear manifold both redirect for "PL manifold".

Contents

Idea

A piecewise-linear manifold, or PL manifold for short, is a manifold whose transition functions are piecewise linear functions?.

See also

Branched covers:

James W. Alexander, Note on Riemann spaces, Bull. Amer. Math. Soc. 26 (1920) 370–373

All PL 4-manifolds are simple branched covers of the 4-sphere:

Riccardo Piergallini, Four-manifolds as 4-fold branched covers of $S^4$ , Topology Volume 34, Issue 3, July 1995 (doi:10.1016/0040-9383(94)00034-I, pdf)
Massimiliano Iori, Riccardo Piergallini, 4-manifolds as covers of the 4-sphere branched over non-singular surfaces, Geom. Topol. 6 (2002) 393-401 (arXiv:math/0203087)

The n-torus for $n \geq 3$ is not a cyclic branched cover of the n-sphere:

U. Hirsch, W. D. Neumann, On cyclic branched coverings of spheres, Math. Ann. (1975) 215: 289 (doi:10.1007/BF01343895)

Last revised on August 1, 2021 at 12:31:23. See the history of this page for a list of all contributions to it.