Parallelizability of Finite H-Spaces.
Parallelizability of Proper Actions, Global K-slices and Maximal Compact Subgroups.
Parametrized Borsuk-Ulam problem for projective space bundles
Let π: E → B be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let π’: E’ → B be a vector bundle such that ℤ₂ acts fiber preserving and freely on E and E’-0, where 0 stands for the zero section of the bundle π’: E’ → B. For a fiber preserving ℤ₂-equivariant map f: E → E’, we estimate the cohomological dimension of the zero set . As an application, we also estimate the cohomological dimension of the ℤ₂-coincidence set of a fiber preserving...
Parametrized Borsuk-Ulam theorems.
Periodic equivariant Real k-theories have rational Tate theory.
Periodische Homöomorhismen Seifertscher Faserräume.
p-Nilpotence, classifying space indecomposability, and other properties of almost all finite groups.
Poincaré Spaces, Their Normal Fibrations and Surgery.
Poincaré submersions.
Polynomial structures on principal fibre bundles
Positivity of Schur function expansions of Thom polynomials
Combining the approach to Thom polynomials via classifying spaces of singularities with the Fulton-Lazarsfeld theory of cone classes and positive polynomials for ample vector bundles, we show that the coefficients of the Schur function expansions of the Thom polynomials of stable singularities are nonnegative with positive sum.
Positivity of Thom polynomials II: the Lagrange singularities
We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of the Thom polynomials of Lagrange singularities always have nonnegative coefficients. This is an analog of a result on the Thom polynomials of mapping singularities and Schur S-functions, established formerly by the last two authors.
Postnikov Towers Associated with Complex 2-Plane and Symplectic Line Bundles.
Principal bundles with parabolic structure.
Principal fibre bundles with structural Lie groupoid.
Product splittings for p-compact groups
We show that a connected p-compact group with a trivial center is equivalent to a product of simple p-compact groups. More generally, we show that product splittings of any connected p-compact group correspond bijectively to algebraic splittings of the fundamental group of the maximal torus as a module over the Weyl group. These are analogues for p-compact groups of well-known theorems about compact Lie groups.
Prolongation of natural bundles