A Converse to a Residual Finiteness Theorem of G. Baumslag

A Converse to Dye’s Theorem

Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of F2 on a standard Borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces. There is a treeable non-hyperfinite Borel equivalence relation which is not univ...

A Converse to a Theorem of Adamyan, Arov and Krein

A classical theorem of Pick gives a criterion for interpolation by analytic functions in the open unit disc D subject to an H∞-norm bound. This result has substantial generalizations in two different directions. On the one hand, one can replace H∞ by the multiplier algebras of certain Hilbert function spaces, some of them having no connection with analyticity [Ag1, Ag2]. On the other hand, one ...

Ribet’s Converse to Herbrand’s Theorem

Classes of Groups Generalizing a Theorem of Benjamin Baumslag

In [BB] Benjamin Baumslag proved that being fully residually free is equivalent to being residually free and commutative transitive (CT). Gaglione and Spellman [GS] and Remeslennikov [Re] showed that this is also equivalent to being universally free, that is, having the same universal theory as the class of nonabelian free groups. This result is one of the cornerstones of the proof of the Tarks...

On the Converse to a Theorem of Atiyah and Bott

Throughout this paper, C denotes a smooth projective curve of genus at least one, G denotes a reductive linear algebraic group over C, and ξ0 is a C ∞ principal G-bundle over C. The space of all (0, 1)-connections on ξ0 is an affine space A = A(ξ0) associated to the infinite dimensional complex vector space H0,1(C; ad ξ0). Following Shatz [6] for the case G = GL(n), Atiyah and Bott [1] defined ...