Objective
Low-dimensional topology is a central and exciting area of 21st century research mathematics that has enjoyed a period of intense activity in recent years. On the one hand, steady progress in understanding the deep connections between group theory and three-manifold topology has led to the resolution of long-standing conjectures; on the other, the introduction of modern homological invariants (e.g. Heegaard Floer homology, Khovanov homology) have contributed new insight and perspective on old problems in low-dimensional topology while establishing a vibrant and active field of research exhibiting new ties to physics (e.g. recent work of Witten). This project will treat a major open problem, raised by Ozsvath and Szabo, that is positioned at the nexus of these two areas:
PROBLEM: Establish a relationship between the fundamental group of a three-manifold and its Heegaard Floer theory.
Heegaard Floer homology presents a new tool -- with origins in physics and gauge theory -- for investigating orientable three-manifolds that is both extremely powerful and inherently different from the fundamental group. While there are certainly hints that some aspects of the fundamental group might be captured by Heegaard Floer homology, perhaps the most surprising potential connection is formulated in joint work with Boyer and Gordon:
CONJECTURE: An irreducible three-manifold is an L-space if and only if its fundamental group is not left-orderable.
L-spaces are rational homology spheres with simplest-possible Heegaard Floer homology while left-ordersare auxiliary structures on a group. This project will make major progress on the PROBLEM above by approaching this CONJECTURE from a range of perspectives. It will employ and draw on techniques from representation theory and foliations, and make essential use of the most recent developments in Heegaard Floer theory and left-orderable groups. The results of the project will constitute major progress in low-dimensional topology.
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
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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.
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.
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.
FP7-PEOPLE-2013-CIG
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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.
MC-CIG - Support for training and career development of researcher (CIG)
Coordinator
G12 8QQ Glasgow
United Kingdom
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.