an:03852048
Zbl 0536.57023
Matsumoto, Shigenori; Morita, Shigeyuki
Bounded cohomology of certain groups of homeomorphisms
EN
Proc. Am. Math. Soc. 94, 539-544 (1985).
00148786
1985
j
57T20 55N99 20J05 58D05
\(\ell^ 1\) homology; real cohomology of groups; bounded cohomology of the group of homeomorphisms of real n-space with compact support; bounded cohomology of SL(2,R)
The authors consider relations among bounded cohomology, \(\ell^ 1\) homology and ordinary real cohomology of spaces or groups. They present in particular a necessary and sufficient condition for bounded cohomology to inject into ordinary cohomology and by using it they prove the vanishing of bounded cohomology and \(\ell^ 1\) homology of \(Homeo_ k({\mathbb{R}}^ n)\), the group of all the homeomorphisms of \({\mathbb{R}}^ n\) with compact supports. They also determine the second bounded cohomology of \(SL_ 2{\mathbb{R}}\).
Reviewer (Berlin)