Syzygies in equivariant cohomology for non-abelian Lie groups

We extend the work of Allday-Franz-Puppe on syzygies in equivariant cohomology from tori to arbitrary compact connected Lie groups G. In particular, we show that for a compact orientable G-manifold X the analogue of the Chang-Skjelbred sequence is exact if and only if the equivariant cohomology of X is reflexive, if and only if the equivariant Poincare pairing for X is perfect. Along the way we establish that the equivariant cohomology modules arising from the orbit filtration of X are Cohen-Macaulay. We allow singular spaces and introduce a Cartan model for their equivariant cohomology. We also develop a criterion for the finiteness of the number of infinitesimal orbit types of a G-manifold.Comment: 28 pages; minor change

Equivariant cohomology and analytic descriptions of ring isomorphisms

In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a $G$-manifold in terms of algebra, so that we can obtain analytic descriptions of ring isomorphisms among equivariant cohomology rings of such $G$-manifolds, and a necessary and sufficient condition that the equivariant cohomology rings of such two $G$-manifolds are isomorphic. This also leads us to analyze how many there are equivariant cohomology rings up to isomorphism for such $G$-manifolds in 2- and 3-dimensional cases.Comment: 20 pages, updated version with two references adde

Is every toric variety an M-variety?

A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coincides with the corresponding sum for the real part of X. It has been known for a long time that any nonsingular complete toric variety is an M-variety. In this paper we consider whether this remains true for toric varieties that are singular or not complete, and we give a positive answer when the dimension of X is less than or equal to 3.Comment: 13 page

Orbit spaces of free involutions on the product of two projective spaces

Let $X$ be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on $X$ and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the Leray spectral sequence associated to the Borel fibration $X \hookrightarrow X_{\mathbb{Z}_2} \longrightarrow B_{\mathbb{Z}_2}$. We also give an application of our result to show that if $X$ has the mod 2 cohomology algebra of the product of two real projective spaces (respectively complex projective spaces), then there does not exist any $\mathbb{Z}_2$-equivariant map from $\mathbb{S}^k \to X$ for $k \geq 2$ (respectively $k \geq 3$), where $\mathbb{S}^k$ is equipped with the antipodal involution.Comment: 14 pages, to appear in Results in Mathematic

Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

Genome Diversity of Epstein-Barr Virus from Multiple Tumor Types and Normal Infection

Epstein-Barr virus (EBV) infects most of the world’s population and is causally associated with several human cancers, but little is known about how EBV genetic variation might influence infection or EBV-associated disease. There are currently no published wild-type EBV genome sequences from a healthy individual and very few genomes from EBV-associated diseases. We have sequenced 71 geographically distinct EBV strains from cell lines, multiple types of primary tumor, and blood samples and the first EBV genome from the saliva of a healthy carrier. We show that the established genome map of EBV accurately represents all strains sequenced, but novel deletions are present in a few isolates. We have increased the number of type 2 EBV genomes sequenced from one to 12 and establish that the type 1/type 2 classification is a major feature of EBV genome variation, defined almost exclusively by variation of EBNA2 and EBNA3 genes, but geographic variation is also present. Single nucleotide polymorphism (SNP) density varies substantially across all known open reading frames and is highest in latency-associated genes. Some T-cell epitope sequences in EBNA3 genes show extensive variation across strains, and we identify codons under positive selection, both important considerations for the development of vaccines and T-cell therapy. We also provide new evidence for recombination between strains, which provides a further mechanism for the generation of diversity. Our results provide the first global view of EBV sequence variation and demonstrate an effective method for sequencing large numbers of genomes to further understand the genetics of EBV infection

The stable free rank of symmetry of products of spheres

A well known conjecture in the theory of transformation groups states that if p is a prime and (Z/p)^r acts freely on a product of k spheres, then r is less than or equal to k. We prove this assertion if p is large compared to the dimension of the product of spheres. The argument builds on tame homotopy theory for non simply connected spaces.Comment: 30 pages; improved exposition, some details adde

Epstein-Barr virus ensures B cell survival by uniquely modulating apoptosis at early and late times after infection

Abstract Latent Epstein-Barr virus (EBV) infection is causally linked to several human cancers. EBV expresses viral oncogenes that promote cell growth and inhibit the apoptotic response to uncontrolled proliferation. The EBV oncoprotein LMP1 constitutively activates NFkB and is critical for survival of EBV-immortalized B cells. However, during early infection EBV induces rapid B cell proliferation with low levels of LMP1 and little apoptosis. Therefore, we sought to define the mechanism of survival in the absence of LMP1/NFkB early after infection. We used BH3 profiling to query mitochondrial regulation of apoptosis and defined a transition from uninfected B cells (BCL-2) to early-infected (MCL-1/BCL-2) and immortalized cells (BFL-1). This dynamic change in B cell survival mechanisms is unique to virus-infected cells and relies on regulation of MCL-1 mitochondrial localization and BFL-1 transcription by the viral EBNA3A protein. This study defines a new role for EBNA3A in the suppression of apoptosis with implications for EBV lymphomagenesis

Multiplicity distributions at high energies as a sum of Poissonian-like distributions

It is shown that at collider energies experimental multiplicity distributions are well parameterized by a sum of Gupta-Sarma distributions. This extends earlier description of the lower energy data by the two parameter sum of Poissonians. Implications of the proposed parametrization for LHC are discussed.Comment: 16 pages, Latex, 4 EPS figure