manifolds and cobordisms
cobordism theory, Introduction
A manifold is a topological space that is locally isomorphic to a Cartesian space $\mathbb{R}^n$.
A manifold with boundary is a topological space that is locally isomorphic either to an $\mathbb{R}^n$ or to a half-space $H^n = \{ \vec x \in \mathbb{R}^n | x^n \geq 0\}$.
A manifold with corners is a topological space that is locally isomorphic to an $H^n_i = \{ \vec x \in \mathbb{R}^n | x^{i+1}, \cdots, x^n \geq 0\}$ for $0 \leq i \leq n$.
For details see at manifold.
(manifolds with boundaries and corners form full subcategory of diffeological spaces)
The evident functor
from the category of smooth manifolds with boundaries and corners to that of diffeological spaces is fully faithful, hence is a full subcategory-embedding.
(Iglesias-Zemmour 13, 4.16, Gürer & Iglesias-Zemmour 19)
Dominic Joyce, On manifolds with corners (arXiv:0910.3518)
The full subcategory-embedding of manifolds with boundaries and corners into that of diffeological spaces is discussed in:
Patrick Iglesias-Zemmour, section 4.16 of Diffeology, Mathematical Surveys and Monographs, AMS (2013) (web, publisher)
Serap Gürer, Patrick Iglesias-Zemmour, Differential forms on corners, 2017 (pdf)
Serap Gürer, Patrick Iglesias-Zemmour, Differential forms on manifolds with boundary and corners, Indagationes Mathematicae, Volume 30, Issue 5, September 2019, Pages 920-929 (doi:10.1016/j.indag.2019.07.004)
Last revised on December 19, 2019 at 23:29:13. See the history of this page for a list of all contributions to it.