Positively curved GKM-manifolds

Let T be a torus of dimension at least k and M a T-manifold. M is a GKM_k-manifold if the action is equivariantly formal, has only isolated fixed points, and any k weights of the isotropy representation in the fixed points are linearly independent. In this paper we compute the cohomology rings with real and integer coefficients of GKM_3- and GKM_4-manifolds which admit invariant metrics of positive sectional curvature.Comment: 19 pages, 7 figures. Final version, to appear in IMR

Positively oriented matroids are realizable

We prove da Silva's 1987 conjecture that any positively oriented matroid is a positroid; that is, it can be realized by a set of vectors in a real vector space. It follows from this result and a result of the third author that the positive matroid Grassmannian (or positive MacPhersonian) is homeomorphic to a closed ball.Comment: 20 pages, 3 figures, references adde

Positively curved Killing foliations via deformations

We show that a compact manifold admitting a Killing foliation with positive transverse curvature fibers over finite quotients of spheres or weighted complex projective spaces, provided that the singular foliation defined by the closures of the leaves has maximal dimension. This result is obtained by deforming the foliation into a closed one while maintaining transverse geometric properties, which allows us to apply results from the Riemannian geometry of orbifolds to the space of leaves. We also show that the basic Euler characteristic is preserved by such deformations. Using this fact we prove that a Riemannian foliation of a compact manifold with finite fundamental group and nonvanishing Euler characteristic is closed. As another application we obtain that, for a positively curved Killing foliation of a compact manifold, if the structural algebra has sufficiently large dimension then the basic Euler characteristic is positive.Comment: 23 pages, several corrections, results have change

Bacteriochlorophyll aggregates in positively charged micelles

Micellar complexes were prepared from bacteriochlorophyll a and bacteriopheophytin a with the cationic detergents, cetyltrimethyl ammonium bromide and cetylpyridinium chloride. These complexes have spectroscopic properties (absorption, circular dichroism) which are very different from the ones formed with non-ionic detergents like Triton X-100, and also with anionic detergents. Bacteriochlorophyll a forms two complexes: One is blue-shifted and has excitonically coupled Qy transitions. The second one is extremely red-shifted. The unusual properties are suggested to result from interactions of the positively charged head-group of the detergent with the tetrapyrrole

Positively curved manifolds with large spherical rank

Rigidity results are obtained for Riemannian $d$-manifolds with $\sec \geqslant 1$ and spherical rank at least $d-2>0$. Conjecturally, all such manifolds are locally isometric to a round sphere or complex projective space with the (symmetric) Fubini--Study metric. This conjecture is verified in all odd dimensions, for metrics on $d$-spheres when $d \neq 6$, for Riemannian manifolds satisfying the Raki\'c duality principle, and for K\"ahlerian manifolds.Comment: 33 page