Opened 2 years ago

# Manifolds with boundary — at Version 9

Reported by: Owned by: Matthias Köppe major sage-wishlist geometry Eric Gourgoulhon, Dima Pasechnik, Yuan Zhou, Michael Jung N/A

(from #30061)

We propose to add manifolds with boundary to `sage.manifolds`.

Simple examples of topological manifolds with boundary include convex polyhedra and semialgebraic sets with non-singular boundary. These are (except in special cases) not differentiable manifolds, but only "piecewise differentiable" ("manifolds with corners").

References:

### comment:1 Changed 2 years ago by Matthias Köppe

Cc: Dima Pasechnik Yuan Zhou added modified (diff)

### comment:3 Changed 19 months ago by Michael Jung

Perhaps it is better to implement manifolds with corners right away since manifolds with boundaries are just a special case.

### comment:4 Changed 19 months ago by Matthias Köppe

https://arxiv.org/pdf/0910.3518.pdf (Remark 2.11) has a nice overview over several inequivalent definitions of manifolds with corners.

I haven't checked the details yet but I would be interested in a definition that generalizes all polyhedra, including those with degenerate vertices such as the top of the square pyramid in R3. The main definition in this paper, 2.1(iii), does not fit the bill; it would only include simple polyhedra.

A newer article by the same author: https://www.sciencedirect.com/science/article/pii/S0001870816307186 on manifolds with "generalized corners" ("g-corners")

Last edited 19 months ago by Matthias Köppe (previous) (diff)

### comment:5 follow-ups:  6  7 Changed 19 months ago by Dima Pasechnik

hmm, what is "the top of the square pyramid in R3" ?

Do you mean to say that you'd like a definition that includes all the non-simple polytopes, at least?

(vertices of non-convex polyhedra are a different story, much more complicated)

### comment:6 in reply to:  5 Changed 19 months ago by Matthias Köppe

Do you mean to say that you'd like a definition that includes all the non-simple polytopes, at least?

Yes