A Topology on Milnor’s Group of a Topological Field and Continuous Joint Determinants

Abstract EN

For the tuple set of commuting invertible matrices with coefficients in a given field, the joint determinants are defined as generalizations of the determinant map for the square matrices.

We introduce a natural topology on Milnor’s K-groups of a topological field as the quotient topology induced by the joint determinant map and investigate the existence of a nontrivial continuous joint determinant by utilizing this topology, generalizing the author’s previous results on the continuous joint determinants for the commuting invertible matrices over R and C.