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 $H^n_i = \{ \vec x \in \mathbb{R}^n | x^i , x^{i+1}, \cdots, x^n \geq 0\}$ for $0 \leq i \leq n$.
For details see at manifold.
(manifolds with boundary form full subcategory of diffeological spaces)
The evident functor
from the category of smooth manifolds with boundary to that of diffeological spaces is fully faithful, hence is a full subcategory-embedding.
Dominic Joyce, On manifolds with corners (arXiv:0910.3518)
The full subcategory-embedding of manifolds with boundary into that of diffeological spaces is discussed in
Related discussion to the case of manifolds with corners is in
Last revised on June 17, 2019 at 07:24:28. See the history of this page for a list of all contributions to it.