Some hermitian K-groups via geometric topology

Periodicity of Hermitian K-groups

Bott periodicity for the unitary and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic K-groups with …nite coe¢ cients, similar results are consequences of the Milnor and Bloch-Kato conjectures, a¢ rmed by Voevodsky, Rost and others. More generally, we prove that periodicity of the algebraic K-groups for any ring implies periodici...

Periodicity of Hermitian K-theory and Milnor’s K-groups

One purpose of this paper is to improve the periodicity theorem of Hermitian K-theory proved in [6 ], using some recent results by A..J. Berrick and the author [1]. For instance, if 1/2 [ A we show that the “higher Witt groups” εWn(A), defined for a ring A with antiinvolution (ε being the sign of symmetry), are periodic of period α ≠ 0 mod. 4, with a control of the 2-torsion depending on α. Mor...

Some Results in Geometric Topology and Geometry

A representation for some groups, a geometric approach

‎In the present paper‎, ‎we are going to use geometric and topological concepts‎, ‎entities and properties of the‎ ‎integral curves of linear vector fields‎, ‎and the theory of differential equations‎, ‎to establish a representation for some groups on $R^{n} (ngeq 1)$‎. ‎Among other things‎, ‎we investigate the surjectivity and faithfulness of the representation‎. At the end‎, ‎we give some app...

A Geometric Construction for Some Ovoids of the Hermitian Surface

Multiple derivation of the classical ovoid of the Hermitian surface H(3, q) of PG(3, q) is a well known, powerful method for constructing large families of non classical ovoids of H(3, q). In this paper, we shall provide a geometric costruction of a family of ovoids amenable to multiple derivation. Mathematics Subject Classification (2000). Primary 51E20; Secondary 51A50.