Dehn filling of the "magic" 3-manifold

We classify all the non-hyperbolic Dehn fillings of the complement of the chain-link with 3 components, conjectured to be the smallest hyperbolic 3-manifold with 3 cusps. We deduce the classification of all non-hyperbolic Dehn fillings of infinitely many 1-cusped and 2-cusped hyperbolic manifolds, including most of those with smallest known volume. Among other consequences of this classification, we mention the following: - for every integer n we can prove that there are infinitely many hyperbolic knots in the 3-sphere having exceptional surgeries n, n+1, n+2, n+3, with n+1, n+2 giving small Seifert manifolds and n, n+3 giving toroidal manifolds; - we exhibit a 2-cusped hyperbolic manifold that contains a pair of inequivalent knots having homeomorphic complements; - we exhibit a chiral 3-manifold containing a pair of inequivalent hyperbolic knots with orientation-preservingly homeomorphic complements; - we give explicit lower bounds for the maximal distance between small Seifert fillings and any other kind of exceptional filling.Comment: 56 pages, 10 figures, 16 tables. Some consequences of the classification adde

A New Decomposition Theorem for 3-Manifolds

Let M be a (possibly non-orientable) compact 3-manifold with (possibly empty) boundary consisting of tori and Klein bottles. Let $X\subset\partial M$ be a trivalent graph such that $\partial M\setminus X$ is a union of one disc for each component of $\partial M$. Building on previous work of Matveev, we define for the pair (M,X) a complexity c(M,X) and show that, when M is closed, irreducible and P^2-irreducible, $c(M,\emptyset)$ is the minimal number of tetrahedra in a triangulation of M. Moreover c is additive under connected sum, and, given any n>=0, there are only finitely many irreducible and P^2-irreducible closed manifolds having complexity up to n. We prove that every irreducible and P^2-irreducible pair (M,X) has a finite splitting along tori and Klein bottles into pairs having the same properties, and complexity is additive on this splitting. As opposed to the JSJ decomposition, our splitting is not canonical, but it involves much easier blocks than all Seifert and simple manifolds. In particular, most Seifert and hyperbolic manifolds appear to have non-trivial splitting. In addition, a given set of blocks can be combined to give only a finite number of pairs (M,X). Our splitting theorem provides the theoretical background for an algorithm which classifies 3-manifolds of any given complexity. This algorithm has been already implemented and proved effective in the orientable case for complexity up to 9.Comment: 32 pages, 16 figure

Direct Democracy, Political Delegation, and Responsibility Substitution

Can direct democracy provisions improve welfare over pure representative democracy? This paper studies how such provisions affect politicians’ incentives and selection. While direct democracy allows citizens to correct politicians’ mistakes, it also reduces the incentives of elected representatives to search for good policies. This responsibility substitution reduces citizens’ ability to screen competent politicians, when elections are the only means to address political agency problems. A lower cost of direct democracy induces a negative spiral on politicians incentives, which we characterize by a disincentive multiplier. As a consequence, introducing initiatives or lowering their cost can reduce voters’ expected utility. Moreover, when elections perform well in selecting politicians and provide incentives, this indirect welfare reducing effect is stronger.Direct Democracy, Initiative, Referendum, Political Agency, Delegation JEL Classification Numbers: D72, D78, P16

Dehn filling of cusped hyperbolic 3-manifolds with geodesic boundary

We define for each g>=2 and k>=0 a set M_{g,k} of orientable hyperbolic 3-manifolds with $k$ toric cusps and a connected totally geodesic boundary of genus g. Manifolds in M_{g,k} have Matveev complexity g+k and Heegaard genus g+1, and their homology, volume, and Turaev-Viro invariants depend only on g and k. In addition, they do not contain closed essential surfaces. The cardinality of M_{g,k} for a fixed k has growth type g^g. We completely describe the non-hyperbolic Dehn fillings of each M in M_{g,k}, showing that, on any cusp of any hyperbolic manifold obtained by partially filling M, there are precisely 6 non-hyperbolic Dehn fillings: three contain essential discs, and the other three contain essential annuli. This gives an infinite class of large hyperbolic manifolds (in the sense of Wu) with boundary-reducible and annular Dehn fillings having distance 2, and allows us to prove that the corresponding upper bound found by Wu is sharp. If M has one cusp only, the three boundary-reducible fillings are handlebodies.Comment: 28 pages, 16 figure

Transfer of metal ions at the soil-root interface: role of VO²⁺ on Fe³⁺ mobilization from a Fe(III)-network

This note reports the role of VO(IV) on Fe(III) mobilization from a Fe(III)-polygalacturonate network. The effect of the reaction on the physical properties of the system is also considered