Opened 5 years ago

Last modified 4 years ago

#18529 closed enhancement

Topological manifolds: basics — at Version 9

Reported by: egourgoulhon Owned by: egourgoulhon
Priority: major Milestone: sage-7.1
Component: geometry Keywords: topological manifolds
Cc: mmancini Merged in:
Authors: Eric Gourgoulhon Reviewers:
Report Upstream: N/A Work issues:
Branch: public/manifolds/top_manif_basics Commit: fb96562c1e7d4ffc76ca87efcc15d133c6c15190
Dependencies: #18175 Stopgaps:

Description (last modified by egourgoulhon)

This is the implementation of topological manifolds over a topological field K resulting from the SageManifolds project. See the meta-ticket #18528 for an overview. By topological manifold over a topological field K it is meant a second countable Hausdorff space M such that every point in M has a neighborhood homeomorphic to Kn, with the same non-negative integer n for all points.

This tickets implements the following Python classes:

  • TopManifold: topological manifold over a topological field K
  • TopManifoldPoint: point in a topological manifold
  • TopManifoldSubset: generic subset of a topological manifold
  • Chart: chart of a topological manifold
    • RealChart: chart of a topological manifold over the real field
  • CoordChange: transition map between two charts of a topological manifold

TopManifold is intended to serve as a base class for specific manifolds, like smooth manifolds (K=R) and complex manifolds (K=C).

Change History (9)

comment:1 Changed 5 years ago by egourgoulhon

  • Description modified (diff)

comment:2 follow-up: Changed 5 years ago by jhpalmieri

The phrase "manifold over a field K" sounds odd to me. Is it used in the literature? What if K is a finite field? It seems that if X is a finite discrete space, for every finite field F and for every non-negative integer n, then X is a manifold over F of dimension n: F and n play no role. (I'm assuming that finite fields have been given the discrete topology.)

I think you might say "topological manifold over a topological field K", since obviously the topology on K is critical. Or you could omit "over a field K", and mention in the documentation that users can specify a topological field (like \CC, rather than the default \RR) if they want.

comment:3 Changed 5 years ago by egourgoulhon

  • Description modified (diff)

comment:4 in reply to: ↑ 2 Changed 5 years ago by egourgoulhon

Replying to jhpalmieri:

The phrase "manifold over a field K" sounds odd to me. Is it used in the literature?

Thanks for your comment. You are right: this is an abusive generalization of "manifold over R" and "manifold over C", which are used in the literature.

What if K is a finite field? It seems that if X is a finite discrete space, for every finite field F and for every non-negative integer n, then X is a manifold over F of dimension n: F and n play no role. (I'm assuming that finite fields have been given the discrete topology.)

I think you might say "topological manifold over a topological field K", since obviously the topology on K is critical. Or you could omit "over a field K", and mention in the documentation that users can specify a topological field (like \CC, rather than the default \RR) if they want.

Thanks for your suggestion; I've modified the ticket description accordingly. I've also added what is meant by "topological manifold over a topological field K".

PS: note that the code in the associated branch is still in a very crude draft state, but should be ready for review within a few days.

Last edited 5 years ago by egourgoulhon (previous) (diff)

comment:5 Changed 5 years ago by git

  • Commit changed from 89c063c7119f19497e3d21b2a5a9dcb0752122b0 to 5a5722b4a0ef33d8624fdd127bbb1964232ced96

Branch pushed to git repo; I updated commit sha1. New commits:

5a5722bAdd doctests in classes Chart and RealChart

comment:6 Changed 5 years ago by git

  • Commit changed from 5a5722b4a0ef33d8624fdd127bbb1964232ced96 to 4f490af5fedeb0a28dd8ddab70efdab1cc64bf93

Branch pushed to git repo; I updated commit sha1. New commits:

4f490afImprove the documentation of coordinate charts

comment:7 Changed 5 years ago by git

  • Commit changed from 4f490af5fedeb0a28dd8ddab70efdab1cc64bf93 to d8df59f286da79e1e103b56064fdffb702e034ce

Branch pushed to git repo; I updated commit sha1. New commits:

d8df59fImprove the documentation of TopManifold

comment:8 Changed 5 years ago by git

  • Commit changed from d8df59f286da79e1e103b56064fdffb702e034ce to fb96562c1e7d4ffc76ca87efcc15d133c6c15190

Branch pushed to git repo; I updated commit sha1. New commits:

fb96562Open subsets of topological manifolds are now fully considered as topological manifolds.

comment:9 Changed 5 years ago by egourgoulhon

  • Description modified (diff)
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