Volcanological constraints of Archaean tectonics

Volcanological and trace element geochemical data can be integrated to place some constraints upon the size, character and evolutionary history of Archean volcanic plumbing, and hence indirectly, Archean tectonics. The earliest volcanism in any greenhouse belt is almost universally tholeitic basalt. Archean mafic magma chambers were usually the site of low pressure fractionation of olivine, plagioclase and later Cpx + or - an oxide phase during evolution of tholeitic liquids. Several models suggest basalt becoming more contaminated by sial with time. Data in the Uchi Subprovince shows early felsic volcanics to have fractionated REE patterns followed by flat REE pattern rhyolites. This is interpreted as initial felsic liquids produced by melting of a garnetiferous mafic source followed by large scale melting of LIL-rich sial. Rare andesites in the Uchi Subprovince are produced by basalt fractionation, direct mantle melts and mixing of basaltic and tonalitic liquids. Composite dikes in the Abitibi Subprovince have a basaltic edge with a chill margin, a rhyolitic interior with no basalt-rhyolite chill margin and partially melted sialic inclusions. Ignimbrites in the Uchi and Abitibi Subprovinces have mafic pumice toward the top. Integration of these data suggest initial mantle-derived basaltic liquids pond in a sialic crust, fractionate and melt sial. The inirial melts low in heavy REE are melts of mafic material, subsequently melting of adjacent sial produces a chamber with a felsic upper part underlain by mafic magma

Should We Press the Victims: The Uneven Support for International Criminal Tribunals

International criminal tribunals rely on international support. However, in the case of the ICTY and the ICTR, international support has been uneven. I argue that this uneven support is related to the post-atrocity status of the domestic governing authority. In cases where the governing authority retains the status of victim, as in Rwanda following the 1994 Tutsi genocide, the international community has been reluctant to back the ICTR in its attempts to prosecute all participants of the 1994 genocide. In cases where the governing authority retains the status of perpetrator, as in Serbia following the Bosnian genocide of the 1990s, the international community has been more supportive of the ICTY. In cases where the post-atrocity status is mixed, as in Croatia, the backing of the international community of the ICTY has been similarly mixed

Virtual Betti numbers of genus 2 bundles

We show that if M is a surface bundle over S^1 with fiber of genus 2, then for any integer n, M has a finite cover tilde(M) with b_1(tilde(M)) > n. A corollary is that M can be geometrized using only the `non-fiber' case of Thurston's Geometrization Theorem for Haken manifolds.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper19.abs.htm

All flat manifolds are cusps of hyperbolic orbifolds

We show that all closed flat n-manifolds are diffeomorphic to a cusp cross-section in a finite volume hyperbolic (n+1)-orbifold.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-13.abs.htm

The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing vector. In particular, we show that the RG flow with De Turck terms can be reduced to two equations: the continual Toda flow solved by Bakas, plus its linearizaton. We find exact solutions which flow to homogeneous but not always isotropic geometries

On the geometric boundaries of hyperbolic 4-manifolds

We provide, for hyperbolic and flat 3-manifolds, obstructions to bounding hyperbolic 4-manifolds, thus resolving in the negative a question of Farrell and Zdravkovska.Comment: 8 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper5.abs.htm

Spherical structures on torus knots and links

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formul{\ae} are presented.Comment: 17 pages, 5 figures; typo