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Towards symplectic Teichmueller theory

Objective

"Over the last decade, homological algebra has entered symplectic topology, largely thanks to the appearance of Fukaya categories in homological mirror symmetry. Applications of these new methods and ideas are still scarce. We propose a fundamentally new approach to studying symplectic dynamics, by studying the action of the symplectic mapping class group on the complex manifold of stability conditions on its Fukaya category. This can be seen as a first attempt to generalise classical Teichmueller theory to higher-dimensional symplectic manifolds. Many invariants arising in low-dimensional topology, including Khovanov cohomology for knots, are governed by the Fukaya categories of associated moduli spaces. We propose an ""uncertainty principle"" in topology, in which these invariants are intrinsically constrained by rigidity of this underlying categorical structure. Besides applications in topology, this suggests a framework for studying the sense in which topological complexity is the shadow of dynamical complexity."

Field of science

  • /natural sciences/mathematics/pure mathematics/algebra
  • /natural sciences/mathematics/pure mathematics/topology

Call for proposal

ERC-2007-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE
Address
Trinity Lane The Old Schools
CB2 1TN Cambridge
United Kingdom
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 650 000
Principal investigator
Ivan Smith (Dr.)
Administrative Contact
Renata Schaeffer (Ms.)

Beneficiaries (1)

THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE
United Kingdom
EU contribution
€ 650 000
Address
Trinity Lane The Old Schools
CB2 1TN Cambridge
Activity type
Higher or Secondary Education Establishments
Principal investigator
Ivan Smith (Dr.)
Administrative Contact
Renata Schaeffer (Ms.)