An equivariant Novikov conjecture

We discuss and formulate the correct equivariant generalization of the strong Novikov conjecture. This will be the statement that certain G-equivariant higher signatures (living in suitable equivariant K-groups) are invariant under G-maps of manifolds which, nonequivariantly, are homotopy equivalences preserving orientation. We prove this conjecture for manifolds modeled on a complete Riemannian manifold of nonpositive curvature on which G (a compact Lie group) acts by isometries. We also use the theory of harmonic maps to construct (in some cases) G-maps into such model spaces.Dedicated to Alexander GrothendieckPartially supported by NSF Grants DMS 84-00900 and 87-00551.Partially supported by NSF Grant DMS 86-02980, a Presidential Young Investigator Award, and a Sloan Foundation Fellowship.     

Charge separation in ground-state 1,2,4,5-tetra-substituted benzene derivatives

The conditions required for a formal biradical to exist in a zwitterionic form in the ground state are discussed following the recent experimental observation of zwitterionic structure in the ground state of a quinoid molecule (di-tert-butyl derivative of 2,5-diamino-1,4-benzoquinonediimine, I). A unique characteristic of molecules of this class is the fact that they may be considered as being formed by the union of two radicals, each having an odd number of pi electrons. In the case of I, one fragment carries the two amino group having 7 pi electrons; it acts as the electron donor. The other fragment carries the two oxygen atoms (carrying 5 pi electrons) and acts as an electron acceptor. A model that predicts the properties of these systems is presented, based on previous work on non-Kekule hydrocarbons(2,3) and on the electron donating and attracting properties of the donor and acceptor groups, respectively. The zwitterion is formed by an electron transfer leading to two subunits carrying 6 pi electrons each and may become more stable than the triplet biradical even in the gas phase (i.e., in the absence of an external field) if the ionization potential of the donor is small (of the order of 3-4 eV). In some cases solvation in a polar solvent is required to make the zwitterionic form the lowest energy species on the ground-state surface. The 'spacer' between the donor and acceptor groups (which need not be necessarily derived from an aromatic structure) can be varied and influences the overall dipole moment that is calculated in some cases to be quite large (over 20 D in the gas phase).     

Stereochemistry of retro-diel-salder fragmentation in gas-phase ions formed by chemical ionization

Retro Diels Alder fragmentation is highly stereospecific in the diones 1 under chemical ionization conditions, both with methane and isobutane as the reagent gases. Only the cis-isomers yield abundant protonated diene and quinone ions. The isotope effect indicates preferential protonation on a CO oxygen, and a subsequent H-migration prior to the formation of the protonated diene cations in the cis isomers.     

The Radon-split and the Helly-core of a point configuration

We provide a systematic construction of point configurations with incompatible Radon-split and Helly-core. This provides a resolution of problems of Reay and Sierksma, and shows that it is computationally hard to decide the compatibility of the split and core of a configuration. Received 29 June 2000; revised 5 January 2001.     

Positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums

In this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums. These conditions are variations of Bapat-Raghavan and Franklin-Lorenz conditions.     

The quadratic Graver cone, quadratic integer minimization, and extensions

It has been shown in a number of recent papers that Graver bases methods enable to solve linear and nonlinear integer programming problems in variable dimension in polynomial time, resulting in a variety of applications in operations research and statistics. In this article we continue this line of investigation and show that Graver bases also enable to minimize quadratic and higher degree polynomial functions which lie in suitable cones. These cones always include all separable convex polynomials and typically more.