On hyperbolic cohomology classes
classification
🧮 math.GT
math.DG
keywords
classeshyperboliccohomologyatoroidalapplicationclarifycomplexescontext
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We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental group. In degree two we clarify the relation between hyperbolic and atoroidal classes, leading to an application to symplectically atoroidal manifolds.
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