Let M be a negatively curved compact Riemannian manifold with (possibly empty) convex boundary. Every closed differential 2-form ξ ∈ Ω2(M) defines a bounded cocycle cξ ∈ Cb2(M) by integrating ξ over straightened 2-simplices. In particular Barge and Ghys [Invent. Math. 92 (1988), pp. 509–526] proved that, when M is a closed hyperbolic surface, Ω2(M) injects this way in Hb2(M) as an infinite dimensional subspace. We show that the cup product of any class of the form [cξ], where ξ is an exact differential 2-form, and any other bounded cohomology class is trivial in Hb•(M).
Cup product in bounded cohomology of negatively curved manifolds
Marasco, Domenico
2023-01-01
Abstract
Let M be a negatively curved compact Riemannian manifold with (possibly empty) convex boundary. Every closed differential 2-form ξ ∈ Ω2(M) defines a bounded cocycle cξ ∈ Cb2(M) by integrating ξ over straightened 2-simplices. In particular Barge and Ghys [Invent. Math. 92 (1988), pp. 509–526] proved that, when M is a closed hyperbolic surface, Ω2(M) injects this way in Hb2(M) as an infinite dimensional subspace. We show that the cup product of any class of the form [cξ], where ξ is an exact differential 2-form, and any other bounded cohomology class is trivial in Hb•(M).File in questo prodotto:
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