On properties of effective topological complexity and effective Lusternik-Schnirelmann category
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916158171512832 |
|---|---|
| author | Błaszczyk, Zbigniew Baro, Arturo Espinosa Viruel, Antonio |
| author_facet | Błaszczyk, Zbigniew Baro, Arturo Espinosa Viruel, Antonio |
| contents | The notion of effective topological complexity, introduced by Błaszczyk and Kaluba, deals with using group actions in the configuration space in order to reduce the complexity of the motion planning algorithm. In this article we focus on studying several properties of such notion of topological complexity. We introduce a notion of effective LS-category which mimics the behaviour the usual LS-cat has in the non-effective setting. We use it to investigate the relationship between these effective invariants and the orbit map with respect of the group action, and we give numerous examples. Additionally, we investigate non-vanishing criteria based on a cohomological dimension bound of the saturated diagonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18524 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On properties of effective topological complexity and effective Lusternik-Schnirelmann category Błaszczyk, Zbigniew Baro, Arturo Espinosa Viruel, Antonio Algebraic Topology 55M30 (Primary) 68T40 (Secondary) The notion of effective topological complexity, introduced by Błaszczyk and Kaluba, deals with using group actions in the configuration space in order to reduce the complexity of the motion planning algorithm. In this article we focus on studying several properties of such notion of topological complexity. We introduce a notion of effective LS-category which mimics the behaviour the usual LS-cat has in the non-effective setting. We use it to investigate the relationship between these effective invariants and the orbit map with respect of the group action, and we give numerous examples. Additionally, we investigate non-vanishing criteria based on a cohomological dimension bound of the saturated diagonal. |
| title | On properties of effective topological complexity and effective Lusternik-Schnirelmann category |
| topic | Algebraic Topology 55M30 (Primary) 68T40 (Secondary) |
| url | https://arxiv.org/abs/2402.18524 |