Towards Directed Collapsibility (Research)

Robin Belton, Robyn Brooks, Stefania Ebli, Lisbeth Fajstrup, Brittany Terese Fasy, Catherine RAy, Nicole Sanderson, Elizabeth Vidaurre

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationAdvances in Mathematical Sciences : AWM Research Symposium, Houston, TX, April 2019
EditorsBahar Acu, Donatella Danielli, Marta Lewicka, A.N. Pati, S. Ramanathapuram Vancheeswara, M.I. Teboh-Ewungkem
Number of pages17
PublisherSpringer Publishing Company
Publication date14 Jul 2020
ISBN (Print)978-3-030-42686-6
ISBN (Electronic)978-3-030-42686-3
Publication statusPublished - 14 Jul 2020
Event2019 Association for Women in Mathematics (AWM) Research Symposium - Rice University, Houston, United States
Duration: 6 Apr 20197 Apr 2019


Conference2019 Association for Women in Mathematics (AWM) Research Symposium
LocationRice University
Country/TerritoryUnited States
SeriesAssociation for Women in Mathematics Series

Bibliographical note

Publisher Copyright:
© The Author(s) and the Association for Women in Mathematics 2020.


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