Lower-bound conjecture for the moduli group of positive scalar curvature metrics
Lower-bound conjecture for the moduli group of positive scalar curvature metrics
Let be a closed spin manifold with fundamental group and dimension , and suppose that carries a positive scalar curvature metric. Let be the coinvariant moduli group of concordance classes of positive scalar curvature metrics. Define to be the cardinality of the set of positive integers that occur as orders of nontrivial elements of :
Moduli-group rank conjecture. The rank of is at least .
This would give a lower bound for the size of the moduli space of positive scalar curvature metrics after quotienting by diffeomorphisms. The supplied source does not state whether the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Zhizhang Xie and Guoliang Yu, “Higher rho invariants and the moduli space of positive scalar curvature metrics”, arXiv:1310.1136 (2014).
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