Operators with nilpotent $p$-curvature

Indigenous bundles with nilpotent p-curvature

We study indigenous bundles in characteristic p > 0 with nilpotent p-curvature, and show that they corresponds to simpler objects which we call deformation data. We consider the existence problem of a certain class of deformation data, which arise from the reduction of Belyi maps from characteristic zero to characteristic p. Mathematics Subject Classification (2000): Primary 14H25, 14H60.

Curvature in Nilpotent Lie Groups

Colloq. Algebraic Topology, 1962, pp. 104-113, Matematisk Institut, Aarhus Universitet, Denmark. 4. M. F. Atiyah, Thorn complexes, Proc. London Math. Soc. (3) 11 (1961), 291310. 5. M. F. Atiyah and J. A. Todd, On complex Stiefel manifolds, Proc. Cambridge Philos. Soc. 56 (1960), 342-353. 6. Sze-Tsen Hu, Homotopy theory, Pure and Applied Mathematics VIII, Academic Press, New York and London, 195...

Equivalence operators in nilpotent systems

Products of commuting nilpotent operators

Matrices that are products of two (or more) commuting square-zero matrices and matrices that are products of two commuting nilpotent matrices are characterized. Also given are characterizations of operators on an infinite dimensional Hilbert space that are products of two (or more) commuting square-zero operators, as well as operators on an infinite-dimensional vector space that are products of...

Compact Riemannian Manifolds with Positive Curvature Operators

M is said to have positive curvature operators if the eigenvalues of Z are positive at each point p € M. Meyer used the theory of harmonic forms to prove that a compact oriented n-dimensional Riemannian manifold with positive curvature operators must have the real homology of an n-dimensional sphere [GM, Proposition 2.9]. Using the theory of minimal two-spheres, we will outline a proof of the f...