Objective
"Heegaard Floer theory. In this project (in collaboration with P. Ozsváth and Z. Szabó) we plan to extend our earlier results computing various versions of Heegaard Floer homologies purely combinatorially. We also plan to find combinatorial definitions of these invariants (as graded groups). Such results will potentially lead to a combinatorial description of 4-dimensional Heegaard Floer (mixed) invariants, conjecturally equivalent to Seiberg-Witten invariants of smooth 4-manifolds. In particular, we hope to find a combinatorial proof of Donaldson’s diagonalizability theorem, and find relations between the Heegaard Floer and the fundamental groups of a 3-manifold.
Contact topology. Using Heegaard Floer theory and contact surgery, a systematic study of existence of tight contact structures on 3-manifolds is planned. Similar techniques also apply in studying Legendrian and transverse knots in contact 3-manifolds. In particular, the verification of the existence of tight structures on 3-manifolds given by surgery on a knot (with high enough framing) in the 3-sphere is proposed. Using the Legendrian invariant of knots, Legendrian and transverse simplicity can be conveniently studied. The ideas detailed in this part are planned to be carried out partly in collaboration with Paolo Lisca, Vera Vértesi and Hansjörg Geiges.
Exotic 4-manifolds. Extending our previous results, we plan to investigate the existence of exotic smooth structures on 4-manifolds with small Euler characteristics, such as the complex projective plane CP2, its blow-up CP2#CP2-bar, the product of two complex projective lines CP1×CP1 and ultimately the 4-dimensional sphere S4. We plan to investigate the effect of the Gluck transformation. Possible extensions of the rational blow down procedure (successful in producing exotic structures) will be also studied. We plan collaborations with Zoltán Szabó, Daniel Nash and Mohan Bhupal in these questions."
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.
- medical and health sciences clinical medicine surgery
- natural sciences mathematics pure mathematics topology
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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
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
ERC-2011-ADG_20110209
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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.
Host institution
1053 Budapest
Hungary
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.