Topological aspects of symplectic manifolds with symmetries (A01)

• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066

We continue and expand our study of topological properties of symplectic and Kähler manifolds endowed with a compact Lie group action, aiming at information on their equivariant topological invariants. Key objects of study are compact symplectic manifolds with a torus action, and manifolds associated with representations of quivers. More specifically, we will study the topological invariants and diffeomorphism type of compact symplectic manifolds of dimension 6 with a Hamiltonian action of a 2-torus, which goes in the direction of proving a conjecture posed by Fine and Panov, and we will study the Mukai inequality for certain categories of monotone manifolds, using new techniques developed during the first funding period. Moreover, we will continue the development of a GKM type theory for moduli spaces of quiver representations, with applications to Donaldson-Thomas and Gromov-Witten invariants.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 191: Symplectic Structures in Geometry, Algebra and Dynamics
• Applicant Institution: Universität zu Köln
• Co-Applicant Institution: Ruhr-Universität Bochum
• Project Heads: Professor Dr. Peter Heinzner, until 12/2020; Professor Dr. Markus Reineke; Professorin Dr. Silvia Sabatini