- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Morita Invariance of Invariant Topological Complexity
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Morita Invariance of Invariant Topological Complexity Colman, Hellen
Description
We show that the invariant topological complexity defines a new numerical invariant for orbifolds. <br/><br/> Orbifolds may be described as global quotients of spaces by compact group actions with finite isotropy groups. The same orbifold may have descriptions involving different spaces and different groups. We say that two actions are Morita equivalent if they define the same orbifold. Therefore, any notion defined for group actions should be Morita invariant to be well defined for orbifolds. <br/><br/> We use the homotopy invariance of equivariant principal bundles to prove that the equivariant A-category of Clapp and Puppe is invariant under Morita equivalence. As a corollary, we obtain that both the equivariant Lusternik-Schnirelmann category of a group action and the invariant topological complexity are invariant under Morita equivalence. This allows a definition of topological complexity for orbifolds. <br/><br/> This is joint work with Andres Angel, Mark Grant and John Oprea
Item Metadata
Title |
Morita Invariance of Invariant Topological Complexity
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2020-09-18T10:15
|
Description |
We show that the invariant topological complexity defines a new numerical invariant for orbifolds.
<br/><br/>
Orbifolds may be described as global quotients of spaces by compact group actions with finite isotropy groups. The same orbifold may have descriptions involving different spaces and different groups. We say that two actions are Morita equivalent if they define the same orbifold. Therefore, any notion defined for group actions should be Morita invariant to be well defined for orbifolds.
<br/><br/>
We use the homotopy invariance of equivariant principal bundles to prove that the equivariant A-category of Clapp and Puppe is invariant under Morita equivalence. As a corollary, we obtain that both the equivariant Lusternik-Schnirelmann category of a group action and the invariant topological complexity are invariant under Morita equivalence. This allows a definition of topological complexity for orbifolds.
<br/><br/>
This is joint work with Andres Angel, Mark Grant and John Oprea
|
Extent |
44.0 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Wright College
|
Series | |
Date Available |
2021-03-18
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0396158
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Faculty
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International