Project description
Expanding the combinatorial formulations of Heegaard Floer homology
Heegaard Floer homology is a powerful invariant for studying key objects in low-dimensional topology, especially knots and links in 3-manifolds. Given a cobordism between two links, there is an induced map between their Heegaard Floer homologies. The Heegaard Floer homology for knots and links in the three-sphere is algorithmically computable using certain combinatorial approaches. The EU-funded MM-CAHF project has a two-fold objective: expand the combinatorial formulations of Heegaard Floer homology to encompass a wider class of objects, and extend such formulations to cobordism maps, in order to make these maps algorithmically computable too.
Objective
The action's goal is to achieve major advances in Heegaard Floer homology for knots and links. Heegaard Floer homology is a package of powerful invariants for 3-manifolds, and knots and links inside them. Introduced two decades ago, it is now a major research area in low-dimensional topology. To a knot or link in the 3-sphere, together with extra data called `decoration', Heegaard Floer homology associates a bigraded vector space which determines key topological properties of such a knot or link, such as its Alexander polynomial and its Seifert genus. Moreover, given a (decorated) link cobordism between two links, there is a linear map induced between their Heegaard Floer homology. The original definition of Heegaard Floer homology is based on counting pseudo-holomorphic curves in symplectic manifolds, but there exist combinatorial reformulations of the vector spaces associated to decorated knots and links.
The proposal consists of three major projects:
1) Give a combinatorial reformulation of the Heegaard Floer cobordism maps, to make their computation algorithmic, by extending existing combinatorial definitions of the vector spaces associated to decorated knots and links.
2) Extend the most efficient combinatorial reformulation, namely the Kauffman-states functor, from decorated knots to decorated links.
3) Define a combinatorial Heegaard Floer invariant for partially decorated links, for which attempts to give an analytic definition seems unfeasible.
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 pure mathematics topology symplectic topology
- natural sciences mathematics pure mathematics topology algebraic topology
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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.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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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) H2020-MSCA-IF-2019
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1053 Budapest
Hungary
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