Canonical equivariant extensions using classical Hodge theory

Lin and Sjamaar have used symplectic Hodge theory to obtain canonical equivariant extensions for Hamiltonian actions on closed symplectic manifolds that have the strong Lefschetz property. Here we obtain canonical equivariant extensions much more generally by means of classical Hodge theory.Comment: 10 page

A C-Symplectic Free S1-Manifold with Contractible Orbits and Cat = 1/2 Dim

An interesting question in symplectic geometry concerns whether or not a closed symplectic manifold can have a free symplectic circle action with orbits contractible in the manifold. Here we present a c-symplectic example, thus showing that the problem is truly geometric as opposed to topological. Furthermore, we see that our example is the only known example of a c-symplectic manifold having non-trivial fundamental group and Lusternik-Schnirelmann category precisely half its dimension

A C-Symplectic Free S1-Manifold with Contractible Orbits and Cat = 1/2 Dim

An interesting question in symplectic geometry concerns whether or not a closed symplectic manifold can have a free symplectic circle action with orbits contractible in the manifold. Here we present a c-symplectic example, thus showing that the problem is truly geometric as opposed to topological. Furthermore, we see that our example is the only known example of a c-symplectic manifold having non-trivial fundamental group and Lusternik-Schnirelmann category precisely half its dimension

The Viral and Cellular MicroRNA Targetome in Lymphoblastoid Cell Lines

Epstein-Barr virus (EBV) is a ubiquitous human herpesvirus linked to a number of B cell cancers and lymphoproliferative disorders. During latent infection, EBV expresses 25 viral pre-microRNAs (miRNAs) and induces the expression of specific host miRNAs, such as miR-155 and miR-21, which potentially play a role in viral oncogenesis. To date, only a limited number of EBV miRNA targets have been identified; thus, the role of EBV miRNAs in viral pathogenesis and/or lymphomagenesis is not well defined. Here, we used photoactivatable ribonucleoside-enhanced crosslinking and immunoprecipitation (PAR-CLIP) combined with deep sequencing and computational analysis to comprehensively examine the viral and cellular miRNA targetome in EBV strain B95-8-infected lymphoblastoid cell lines (LCLs). We identified 7,827 miRNA-interaction sites in 3,492 cellular 3′UTRs. 531 of these sites contained seed matches to viral miRNAs. 24 PAR-CLIP-identified miRNA:3′UTR interactions were confirmed by reporter assays. Our results reveal that EBV miRNAs predominantly target cellular transcripts during latent infection, thereby manipulating the host environment. Furthermore, targets of EBV miRNAs are involved in multiple cellular processes that are directly relevant to viral infection, including innate immunity, cell survival, and cell proliferation. Finally, we present evidence that myc-regulated host miRNAs from the miR-17/92 cluster can regulate latent viral gene expression. This comprehensive survey of the miRNA targetome in EBV-infected B cells represents a key step towards defining the functions of EBV-encoded miRNAs, and potentially, identifying novel therapeutic targets for EBV-associated malignancies

Rational Whitehead products and a spectral sequence

spectral sequence relating the rational hornology of a simply-connected topological space to its rational homotopy ([3], (6.9)). In order to calculate certain differentials in this spectral sequence, we were led, in Part I of this paper ([1]), to attempt to define higher order rational Whitehead products in terms of certain cycles in DG Li