Idioma:

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Monod, Nicolas ; Nariman, Sam

Inventiones mathematicae, 2023-06, Vol.232 (3), p.1439-1475 [Periódico revisado por pares]

Texto completo disponível

Citações Citado por

Título:
Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups
Autor: Monod, Nicolas ; Nariman, Sam
Assuntos: Homology ; Isomorphism ; Lie groups ; Mathematics ; Mathematics and Statistics ; Polynomials ; Rings (mathematics)
É parte de: Inventiones mathematicae, 2023-06, Vol.232 (3), p.1439-1475
Descrição: We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring generated by the bounded Euler class. These seem to be the first examples of groups for which the entire bounded cohomology can be described without being trivial. We further prove that the C r -diffeomorphisms groups of the circle and of the closed 2-disc have the same bounded cohomology as their homeomorphism groups, so that both differ from the ordinary cohomology of C r -diffeomorphisms when r > 1 . Finally, we determine the low-dimensional bounded cohomology of homeo- and diffeomorphism of the spheres S n and of certain 3-manifolds. In particular, we answer a question of Ghys by showing that the Euler class in H 4 ( Homeo ∘ ( S 3 ) ) is unbounded.
Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
Idioma: Inglês

Voltar para lista de resultados

Resultado 1 Avançar Ir para próxima página