In [Mi4,BrocCM1], Minsky, Brock and Canary gave a proof of Thurston’s Ending Lamination Conjecture for indecomposable hyperbolic 3-manifolds. In this paper, we offer another approach to this which was inspired by the original. Many of the key results are similar, though the overall logic is somewhat different. A possible advantage is that much of the relevant theory of “hierarchies” and other, ...

Primary and strongly primary monoids domains play a central role in the ideal factorization theory of commutative domains. It is well-known that satisfying ascending chain condition on divisorial ideals (e.g., numerical monoids) are primary; multiplicative monoid non-zero elements one-dimensional local domain it if Noetherian. In present paper, we focus study additive submonoids non-negative ra...

A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(π, 1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice D, and there is a simple sufficient condition that implies G is a duality group. The universal covers of ...

We prove that any tame abstract elementary class categorical in a suitable cardinal has an eventually global good frame: a forking-like notion defined on all types of single elements. This gives the first known general construction of a good frame in ZFC. We show that we already obtain a well-behaved independence relation assuming only a superstability-like hypothesis instead of categoricity. T...