Project description
Study investigates smooth 4-manifold topology, curve and surface singularities
The primary goal of the LDTSing project, which has received funding by the Marie Skłodowska-Curie Actions programme, is to leverage techniques from smooth 4-manifolds to study deformations of isolated surface singularities. Specifically, the project will use gauge theoretic invariants and lattice theoretic combinatorial techniques for smoothing rational surface singularities. A conjecture of Kollar regarding a class of rational surface singularities with a unique smoothing will be considered. Another goal is to investigate the properties of the 3D rational homology sphere, such as n-divisibility and torsion.
Objective
The aim of the project is two-fold.
One goal is to employ techniques from smooth 4-dimensional topology in the study of deformations of isolated surface singularities. More specifically the project aims at advancing in the study of smoothings of rational surface singularities by means of gauge-theoretic invariants as well as lattice-theoretic combinatorial techniques. A conjecture of Kollar regarding a class of rational surface singularities with a unique smoothing will be considered. The conjecture has natural symplectic and topological counterparts. The plan consists in proving the topological version and investigating the extent to which this version of the problem can lead to advancements in the original conjecture.
Another primary goal is to investigate properties of the 3-dimensional rational homology sphere group, such as n-divisibility and torsion, via constructions involving rational cuspidal curves in possibly singular homology planes. In this context a first specific goal is producing examples of 3-manifolds which are either Seifert fibered spaces or obtained via Dehn surgery on an algebraic knots which are 2-divisible in the rational homology sphere group. In a similar setting it will be investigated the extent to which rational homology balls bounded by integral surgeries on torus knots can be realized algebraically.
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.
- medical and health sciencesclinical medicinesurgery
- natural sciencesmathematicspure mathematicstopology
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Programme(s)
Funding Scheme
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinator
59000 Lille
France