manifold with boundary

**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 manifold.

**(manifolds with boundary form full subcategory of diffeological spaces)**

The evident functor

$SmthMfdWBdr \overset{\phantom{AAAA}}{\hookrightarrow} DiffeologicalSpaces$

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

- Patrick Iglesias-Zemmour, section 4.16 of
*Diffeology*, Mathematical Surveys and Monographs, AMS (2013) (web, publisher)

Related discussion to the case of manifolds with corners is in

- Serap Gürer, Patrick Iglesias-Zemmour,
*Differential forms on corners*, 2017 (pdf)

Last revised on August 3, 2018 at 12:24:19. See the history of this page for a list of all contributions to it.