Free products with amalgamation and $3$-manifolds

Free Products with Amalgamation and 3-manifolds

Heegaard Splittings of Sufficiently Complicated 3-manifolds Ii: Amalgamation

Let M1 and M2 be compact, orientable 3-manifolds, and M the manifold obtained by gluing some component F of ∂M1 to some component of ∂M2 by a homeomorphism φ. We show that when φ is “sufficiently complicated” then (1) the amalgamation of low genus, unstabilized, boundary-unstabilized Heegaard splittings of Mi is an unstabilized splitting of M , (2) every low genus, unstabilized Heegaard splitti...

Notes on C-free Probability with Amalgamation

As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity results, a version of the central limit theorem and an analogue of the conditionally free R-transform constructed by means of multilinear function series.

Exactness of Universal Free Products of Finite Dimensional C-algebras with Amalgamation

Recall that for C-algebras A and B there are many possible norms on A ⊗ B for which the completion is a C-algebra. In particular there are two standard completions A ⊗min B and A⊗max B corresponding to the ‘smallest’ and ‘largest’ possible tensor norms. We say that A is nuclear if these two tensor products correspond for all C-algebras B. We say that a C-algebra A is exact if given any short ex...

Contractible Open 3-manifolds with Free Covering Translation Groups

This paper concerns the class of contractible open 3-manifolds which are “locally finite strong end sums” of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of another 3-manifold the group of covering translations must be a free group. It follows that such a 3-manifold cannot cover a closed 3-manifold. For each countable f...