Project description
Exploring 3D dynamics with welded braid groups
The study of periodic orbits in three-dimensional (3D) dynamics remains a challenging frontier. While braid group theory has successfully been used to study orbit structures on surfaces, its classical form falls short in three dimensions. Backed by the Marie Skłodowska-Curie Actions programme, the WEB3 project will use welded braid groups, a 3D analogue of classical braids. Specifically, it aims to develop new mathematical tools to analyse the behaviour of periodic points in 3D manifolds, thereby extending the understanding of topological dynamics beyond current limits. By bridging braid group theory with low-dimensional topology, WEB3 promises to open new pathways in the study of dynamical systems, fostering innovation and expanding the mathematical framework used to explore 3D orbit structures.
Objective
The connection between braid group theory and topological dynamics arises from the remarkable applications of braid group theory to the study of the periodic orbit structure of iterated surface homeomorphisms. It began the early 1980s and has since grown into a significant area within the theory of low-dimensional dynamical systems. Braid theory, a very powerful and important tool, has been used extensively, among others, by Boyland, Ghrist, Guaschi, Hall, Matsuoka and Vandervorst for proving that the existence of certain orbits forces the existence of several other orbits and for showing how the orbits are interacting among them.
A central objective of topological dynamics on 3-dimensional manifolds is to comprehend the structure of the orbits of a self-map. While there has been done a lot of research on the complexity of orbit structures in 3-dimensional dynamics, there are not known results that are analogous to the impressive known results about the orbit structure on surfaces that use braid theory. One of the main reasons is that the classical braid group theory is trivial on 3-dimensional manifolds.
To counter this obstacle, WEB3 proposes to use the theory of welded braid groups, which is the three-dimensional analogue of classical braids. The aim of WEB3 is to extend the existing literature concerning the orbit structure of 3-dimensional dynamics and in particular to establish a new machinery for exploring the behavior of periodic points of homeomorphisms of 3-dimensional manifolds. This proposal will have significant and wide impact in the field of low-dimensional topology and topological dynamics by fostering innovation and creating new knowledge.
WEB3 is the most fitting project for enriching the current literature both on braid group theory and on topological dynamics, since it combines knowledge from both of these two fields of mathematics and features the necessary tools for emerging them successfully together.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences mathematics pure mathematics topology algebraic topology
You need to log in or register to use this function
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
-
HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA)
MAIN PROGRAMME
See all projects funded under this programme
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships
See all projects funded under this funding scheme
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) HORIZON-MSCA-2024-PF-01
See all projects funded under this callCoordinator
Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
1081 HV Amsterdam
Netherlands
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.