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Projects / Programmes source: ARIS

Analytic and topological methods in complex geometry and theory of foliations

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Research activity

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 
Keywords
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
Evaluation (rules)
source: COBISS
Evaluation of bibliographic research performance indicators according to ARIS methodology
Citations Citations for bibliographic records in COBIB.SI that are linked to records in citation databases
source: WoS source: Scopus source: COBISS
Researchers (6)
no. Code Name and surname Research area Role Period No. of publications
1.  15126  PhD Barbara Drinovec Drnovšek  Mathematics  Researcher  2004 - 2007  149 
2.  09990  PhD Franc Forstnerič  Mathematics  Head  2004 - 2007  469 
3.  25607  PhD Jure Kališnik  Mathematics  Junior researcher  2006 - 2007  29 
4.  11686  PhD Janez Mrčun  Mathematics  Researcher  2004 - 2007  91 
5.  07680  PhD Tatjana Petek  Mathematics  Researcher  2004 - 2007  129 
6.  18171  PhD Marko Slapar  Mathematics  Researcher  2004 - 2007  123 
Organisations (1)
no. Code Research organisation City Registration number No. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  20,227 
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.
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