Cohomologie L p en degré 1 des espaces homogènes

Abstract

The L p -cohomology in degree 1 of Riemannian homogeneous spaces is computed. It turns out that reduced cohomology does not vanish exactly for spaces quasiisometric to negatively curved homogeneous spaces.

Group approximation in Cayley topology and coarse geometry, III: Geometric property (T)

“…Here we recover a result of Pansu [Pan89] that vanishing of L 2 -Betti numbers is a coarse invariant.…”

“…For this purpose, we develop a cohomology theory for such spaces, in analogy with the cohomology theory for group actions. See [Ele98], Chapter 8 in [Gro93], [Ogu], [Pan89], and Chapter 5 in [Roe03] for relevant results. We first work purely algebraically.…”

Пространства Дифференциальных Форм И Отображения С Контролируемым Искажением

“…Факторпространство H k q,p (M ) введено в рабо-те [25], где также доказано, что оно является инвариантом липшицевых струк-тур многообразий. В работах [26]- [33] можно найти некоторые как аналитиче-ские, так и геометрические аспекты теории L p -когомологий (случай p = q).…”

The first Lp-cohomology of some groups with one end

“…Another result concerning groups with one end was given in [13] where it was shown that if G is a co-compact lattice in Sp(n, 1), thenH 1 (p) (G) = 0 exactly for p > 4n + 2. Before we state our first result we need to define what it means for a Riemannian manifold to be rotationally symmetric.…”