#18175: Implement categories for topological and metric spaces and related
categories
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: categories | Resolution:
Keywords: geometry, | Merged in:
topology, sd67 | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 5796cbd4fd66bdad4df405a4942f47e9d9d9c69a
public/categories/topological_metric_spaces-18175| Stopgaps:
Dependencies: #18174 #17160 |
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Comment (by egourgoulhon):
IMHO, a complex manifold should be a topological manifold over '''C'''
(i.e. locally homeomorphic to '''C'''^n^) with holomorphic transition
maps. In the refactoring/split of !SageManifolds I am preparing in #18528,
I have relaxed the assumption of real manifolds used up to now and have
introduced topological manifolds over a generic topological field, having
in mind complex manifolds, in addition to real ones. In the
implementation, each object of the class `ComplexManifold` could have an
attribute which is an almost complex manifold. The latter would be a real
smooth manifold of dimension 2n with an almost complex structure and would
be implemented as a subclass of `SmoothManifold`.
I have the impression that the category `Manifolds` that you are
introducing in the current ticket is sufficient for this, i.e. it can be
used for any topological manifold over a topological field. I plan to set
the `TopManifold` objects of #18529 in this category. Then, the class
`ComplexManifold` would inherit from `TopManifold` and would be set in the
category `Manifolds.Complex()`.
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:18>
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