Abstract
In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest case is when the space of directed paths is homotopy equivalent to that of a single path; we call this the trivial space of directed paths. Directed spaces that are topologically trivial may have non-trivial spaces of directed paths, which means that information is lost when the direction of these topological spaces is ignored. We define a notion of directed collapsibility in the setting of a directed Euclidean cubical complex using the spaces of directed paths of the underlying directed topological space, relative to an initial or a final vertex. In addition, we give sufficient conditions for a directed Euclidean cubical complex to have a contractible or a connected space of directed paths from a fixed initial vertex. We also give sufficient conditions for the path space between two vertices in a Euclidean cubical complex to be disconnected. Our results have applications to speeding up the verification process of concurrent programming and to understanding partial executions in concurrent programs.
| Originalsprog | Engelsk |
|---|---|
| Titel | Advances in Mathematical Sciences : AWM Research Symposium, Houston, TX, April 2019 |
| Redaktører | Bahar Acu, Donatella Danielli, Marta Lewicka, A.N. Pati, S. Ramanathapuram Vancheeswara, M.I. Teboh-Ewungkem |
| Antal sider | 17 |
| Forlag | Springer Publishing Company |
| Publikationsdato | 14 jul. 2020 |
| Sider | 255-271 |
| ISBN (Trykt) | 978-3-030-42686-6 |
| ISBN (Elektronisk) | 978-3-030-42686-3 |
| DOI | |
| Status | Udgivet - 14 jul. 2020 |
| Begivenhed | 2019 Association for Women in Mathematics (AWM) Research Symposium - Rice University, Houston, USA Varighed: 6 apr. 2019 → 7 apr. 2019 |
Konference
| Konference | 2019 Association for Women in Mathematics (AWM) Research Symposium |
|---|---|
| Lokation | Rice University |
| Land/Område | USA |
| By | Houston |
| Periode | 06/04/2019 → 07/04/2019 |
| Navn | Association for Women in Mathematics Series |
|---|---|
| Vol/bind | 21 |
| ISSN | 2364-5733 |
Bibliografisk note
Funding Information:This research is a product of one of the working groups at the Women in Topology (WIT) workshop at MSRI in November 2017. This workshop was organized in partnership with MSRI and the Clay Mathematics Institute, and was partially supported by an AWM ADVANCE grant (NSF-HRD 1500481). In addition, LF and BTF further collaborated at the Hausdorff Research Institute for Mathematics during the Special Hausdorff Program on Applied and Computational Algebraic Topology (2017). The authors also thank the generous support of NSF. RB is partially supported by the NSF GRFP (grant no. DGE 1649608). BTF is partially supported by NSF CCF 1618605. CR is partially supported by the NSF GRFP (grant no. DGE 1842165). SE is supported by the Swiss National Science Foundation (grant no. 200021-172636)
Funding Information:
Acknowledgements This research is a product of one of the working groups at the Women in Topology (WIT) workshop at MSRI in November 2017. This workshop was organized in partnership with MSRI and the Clay Mathematics Institute, and was partially supported by an AWM ADVANCE grant (NSF-HRD 1500481). In addition, LF and BTF further collaborated at the Hausdorff Research Institute for Mathematics during the Special Hausdorff Program on Applied and Computational Algebraic Topology (2017).
Funding Information:
The authors also thank the generous support of NSF. RB is partially supported by the NSF GRFP (grant no. DGE 1649608). BTF is partially supported by NSF CCF 1618605. CR is partially supported by the NSF GRFP (grant no. DGE 1842165). SE is supported by the Swiss National Science Foundation (grant no. 200021-172636)
Publisher Copyright:
© The Author(s) and the Association for Women in Mathematics 2020.