manifolds and cobordisms
cobordism theory, Introduction
higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
A piecewise-linear manifold, or PL manifold for short, is a manifold whose transition functions are piecewise linear functions?.
See also
Branched covers:
Every $n$-dimensional PL manifold is a branched cover of the n-sphere:
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:
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