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Algebraic characteristic classes for idempotent matrices.

Francisco Gómez — 1992

Publicacions Matemàtiques

This paper contains the algebraic analog for idempotent matrices of the Chern-Weil theory of characteristic classes. This is used to show, algebraically, that the canonical line bundle on the complex projective space is not stably trivial. Also a theorem is proved saying that for any smooth manifold there is a canonical epimorphism from the even dimensional algebraic de Rham cohomology of its algebra of smooth functions onto the standard even dimensional de Rham cohomology of the manifold.

Simplicial types and polynomial algebras

Francisco Gómez — 2002

Archivum Mathematicum

This paper shows that the simplicial type of a finite simplicial complex K is determined by its algebra A of polynomial functions on the baricentric coordinates with coefficients in any integral domain. The link between K and A is done through certain admissible matrix associated to K in a natural way. This result was obtained for the real numbers by I. V. Savel’ev [5], using methods of real algebraic geometry. D. Kan and E. Miller had shown in [2] that A determines the homotopy type of the polyhedron...

On residue formulas for characteristic numbers

Francisco Gómez Ruiz — 2009

Banach Center Publications

We show that coefficients of residue formulas for characteristic numbers associated to a smooth toral action on a manifold can be taken in a quotient field Q ( X , . . . , X r ) . This yields canonical identities over the integers and, reducing modulo two, residue formulas for Stiefel Whitney numbers.

Smooth toral actions on principal bundles and characteristic classes.

M.ª Nieves Alamo AntúnezFrancisco Gómez Ruiz — 1987

Extracta Mathematicae

The purpose of our work is to find explicit formulae for the computation of some characteristic classes of smooth principal bundles P: P --> B, in terms of local invariants at a singular subset AG of B, associated to a smooth action of a compact Lie group G on P. This singular subset, AG, is defined as the set of points x in B whose isotropy subgroups Gx have dimension at least one.

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