A nontrivial locally trivial algebra

Trivial Generators for Nontrivial Fibres

Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in Cn where the fibre is nontrivial, has to exceed n. This is s...

Locally trivial W∗-bundles

Links with Trivial Alexander Module and Nontrivial Milnor Invariants

Cochran constructed many links with Alexander module that of the unlink and some nonvanishing Milnor invariants, using as input commutators in a free group and as an invariant the longitudes of the links. We present a different and conjecturally complete construction, that uses elementary properties of clasper surgery, and a different invariant, the tree-part of the LMO invariant. Our method al...

Tameness of some locally trivial pseudovarieties

Tameness is a strong property of semigroup pseudovarieties related to the membership problem. Let κ be the signature comprising semigroup multiplication and the omega implicit operation. We prove the κ-tameness of the pseudovarieties N, D, K and LI.

Rationally trivial quadratic spaces are locally trivial:III

It is proved the following. Let R be a regular semi-local domain containing a field such that all the residue fields are infinite. Let K be the fraction field of R. If a quadratic space (R, q : R → R) over R is isotropic over K, then there is a unimodular vector v ∈ R such that q(v) = 0. If char(R) = 2, then in the case of even n we assume that q is a non-singular space in the sense of [Kn] and...