Riemann surfaces and spin structures
Riemannian foliations on Manifolds with non-negative curvature.
Riemannian foliations with parallel or harmonic basic forms
In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.
Riemannian manifolds not quasi-isometric to leaves in codimension one foliations
Every open manifold of dimension greater than one has complete Riemannian metrics with bounded geometry such that is not quasi-isometric to a leaf of a codimension one foliation of a closed manifold. Hence no conditions on the local geometry of suffice to make it quasi-isometric to a leaf of such a foliation. We introduce the ‘bounded homology property’, a semi-local property of that is necessary for it to be a leaf in a compact manifold in codimension one, up to quasi-isometry. An essential...
Riemannian manifolds with many Killing vector fields
Rigid versus non-rigid cyclic actions.
Rigidity and crystallographic groups, I.
Rigidity and gluing for Morse and Novikov complexes
We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function. A rigidity result is also proved for the Floer complex of a hamiltonian defined on a closed symplectic manifold with . The rigidity results for these complexes show that the complex of a fixed generic function/hamiltonian is a retract of the Morse (respectively Novikov or Floer) complex of any other sufficiently close generic function/hamiltonian....
Rigidity of hypersurfaces in complex projective space
Rohlin's invariant and gauge theory. II: Mapping tori.
Rohlin's invariant and gauge theory III. Homology 4–tori.
Rotation Numbers of Products of Circle Homeomorphisms.
Rotational Symmetry: Basic Properties and Application to Knot Manifolds.
-bundles and exotic actions
Scalar curvature and connected sums of self-dual 4-manifolds
Under a reasonable vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-manifolds is again self-dual. Here we prove that the same result can be extended to the positive scalar curvature case. This is an analogue of the classical theorem of Gromov–Lawson and Schoen–Yau in the self-dual category. The proof is based on twistor theory.
Scalar curvature, covering spaces, and Seiberg-Witten theory.
Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces
The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.
Scindement d’une équivalence d’homotopie en dimension
Scindements de Hegaard et groupe de homéotopies des petites variétés de Seifert.
Second Chern class and Riemann-Roch for vector bundles on resolutions of surface singularities.