8
votes
2answers
331 views

Converse to Milnor's theorem on manifolds with nonnegative Ricci curvature.

Disclaimer : I suspect the question I am about to ask is really hard, but I just want to know the status of such questions. Thanks to Milnor, we know that the $\pi_1$ any compact manifold with ...
4
votes
1answer
399 views

Recognizing the stablizer of a degenerate three forms in six dimension

Define $Stab^{+}(\Omega )$={ $\phi \in GL^{+}(V)$ : $\phi^{*}\Omega=\Omega$ }. we say three-form $\Omega\in\wedge^{3}V^{*}$ is non-degenerate , if $i_X\Omega\neq 0$ for all $X\in V$-{0} Let $V\cong ...
9
votes
1answer
359 views

Kazhdan's property T for Kahler surfaces

Is it true that the fundamental groups of compact Kahler surfaces have property T if and only if it they are finite? I am having trouble finding counterexamples to this, but maybe that's just me...
0
votes
1answer
262 views

Hyperbolicity of a fundamental group

Let G be the fundamental group of a compact 3-manifold which supports on its interior a complete non positively curved Riemannian metric and is a cilinder near de metric. Is G hyperbolic?