On topological algebra sheaves

Sheaves over Topological Spaces

The category of sheaves over a topological space has a rich internal logic, but they also have a very rich geometric interpretation. In these notes I review the basic notions of sheaves over topological spaces, with an emphasis on the geometry of sheaves. I prove that sheaves are toposes, present the proof of the equivalence between the category of sheaves over X and the set of local homeomorph...

Poincar E Sheaves on Topological Spaces

We deene the notion of a Poincar e complex of sheaves over a topological space. Global surgery invariants of spaces and maps are expressed as the assembly of locally deened surgery invariants. For simplicial complexes we recover the theory of Poincar e cycles of Ranicki. For more general spaces we obtain local surgery invariants in the absence of triangulations.

Witt groups of sheaves on topological spaces

This paper investigates the Witt groups of triangulated categories of sheaves (of modules over a ring R in which 2 is invertible) equipped with Poincare-Verdier duality. We consider two main cases, that of perfect complexes of sheaves on locally compact Hausdorff spaces and that of cohomologically constructible complexes of sheaves on polyhedra. We show that the Witt groups of the latter form a...

Parabolic Sheaves on Surfaces and Affine Lie Algebra Gl N

On Topological Filtration for Triquaternion Algebra

The topological filtration on the Grothendieck group of the Severi-Brauer variety corresponding to a triquaternion algebra is computed. In particular, it is shown that the second Chow group of the variety is torsionfree. Let F be a field, A a central simple F -algebra of degree 8 and exponent 2, X = SB(A) the Severi-Brauer variety of A [2]. Consider the second Chow group CH(X), i.e. the group o...