This is a continuation of part I in the series (in progress) of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of non-displaceable Lagrangian fibers on some compact toric manifolds. We also provide a method of finding all those fibers in arbitrary compact toric manif...

We give necessary and sufficient conditions for the existence of pin ± and spin structures on Riemannian manifolds with holonomy group Z k 2. For any n ≥ 4 (resp. n ≥ 6) we give examples of pairs of compact manifolds (resp. compact orientable manifolds) M1, M2, non homeomorphic to each other, that are Laplace isospectral on functions and on p-forms for any p and such that M1 admits a pin ± (res...

The Fibonacci manifolds and the ten smallest known compact orientable three-dimensional hyperbolic manifolds are obtained as twofold coverings of the three-dimensional sphere. The corresponding branch sets are described. It is shown that every manifold under consideration admits a Heegaard splitting of genus two. In this paper we consider compact orientable hyperbolic three-dimensional manifold...

We compute the L-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds.

The main result of this paper is the $G$-homotopy invariance $G$-index signature operator proper co-compact $G$-manifolds. If $G$ manifolds $X$ and $Y$ are equivalent, then we prove that images their operators by map same in $K$-theory $C^{*}$-algebra group $G$. Neither discreteness locally compact nor freeness action on required, so a generalization classical case closed manifolds. Using can d...

We give results on the L2-Betti numbers and Novikov-Shubin invariants of compact manifolds, especially 3-manifolds. We first study the Betti numbers and Novikov-Shubin invariants of a chain complex of Hilbert modules over a finite von Neumann algebra. We establish inequalities among the Novikov-Shubin invariants of the terms in a short exact sequence of chain complexes. Our algebraic results, a...

Abstract This paper presents a direct and simple proof of result concerning the existence metrics positive Ricci curvature on total space fiber bundles with compact structure groups. In particular, it generalizes puts in unified framework results Nash [12] Poor [15]. With intention disseminating this result,we apply to build new examples manifolds curvature, including whose base consists gradie...