Projects / Programmes
Analytic and topological methods in complex geometry and theory of foliations
Code |
Science |
Field |
Subfield |
1.01.00 |
Natural sciences and mathematics |
Mathematics |
|
Code |
Science |
Field |
P001 |
Natural sciences and mathematics |
Mathematics |
P130 |
Natural sciences and mathematics |
Functions, differential equations |
P150 |
Natural sciences and mathematics |
Geometry, algebraic topology |
analytic geometry, affine manifolds, Stein manifolds, holomorphic mappings, algebraic mappings, foliations, foliation groupoids, Lie groupoids, Lie algebroids, Hopf algebroids, Morse theory, CR singularities, CW complexes
Researchers (6)
Organisations (1)
Abstract
We will investigate the following problems in complex geometry, theory of foliations and Lie grupoids.
1. Construction of holomorphic mappings of Stein manifolds to certain complex and algebraic manifolds (immersions, submersions, locally biholomorphic maps, their transversality properties, maps with prescribed singularities). Forstnerič has recently developed new analytic methods to construct holomorphic submersions and foliations on Stein manifolds. We shall apply them to the construction of mappings of affine manifolds to certain projective algebraic manifolds and in the characterization of Stein manifolds which are Riemann domains over the Euclidean spaces. We shall attempt to solve the central problem in this area concerning the approximation of locally biholomorphic maps by global locally biholomorphic maps onEuclidean spaces.
2. Holomorphic foliations on afine manifolds and their approximation by global foliations.
3. Study of Lie groupoids, in particular foliation groupoids and orbifolds. We shall investigate some algebraic invariants of Lie groupoids and the duality between Lie groupoids, Lie algebroids and Hopf algebroids.
4.Constructions of proper holomorphic maps from the disc and finite Riemann surfaces to almost complex and q-complex manifolds.
5. Precise characterization of real even dimensional manifolds admitting the structure of a Stein manifold and characterization of CW-complexes which are strong deformation retracts of Stein manifolds. Development of the Morse theory for critical points of strongly plurisubharmonc functions. Investigation of CR-singularities of real manifolds in complex manifolds of higher dimension.