Compact holonomy G_2 manifolds need not be formal - Lucia Martin Merchan
Автор: Stony Brook Mathematics
Загружено: 2024-11-02
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Mathematics Department Colloquium
October 31, 2024
Lucia Martin Merchan, University of Waterloo
Compact holonomy G_2 manifolds need not be formal
Compact manifolds with special and exceptional holonomy have constrained cohomological properties. Well-known examples include the hard Lefschetz property and the Hodge decomposition for compact Kaehler manifolds. Formality depends on the rational homotopy type of a manifold, and it implies that the rational homotopy groups are determined by the rational cohomology algebra. The connection between formality and holonomy was found by Deligne, Griffiths, Morgan, and Sullivan, who proved that compact Kaehler manifolds are formal. Their result led to the conjecture that all compact manifolds with special and exceptional holonomy should be formal. In this talk, we discuss an example that disproves the conjecture for compact holonomy G_2 manifolds. No prior knowledge about G_2 geometry or formality will be assumed.
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