Marisa Fernández

Symplectic manifolds with no kahler structure

On decrit plusieurs familles de varietes symplectiques compactes qui generalisent la variete de Kodaira-Thurston

Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology

We consider a special class of compact complex nilmanifolds, which we call compact nilmanifolds with nilpotent complex structure. It is shown that if Γ\G is a compact nilmanifold with nilpotent complex structure, then the Dolbeault cohomology H∗,∗ ∂̄ (Γ\G) is canonically isomorphic to the ∂̄–cohomology H∗,∗ ∂̄ (gC) of the bigraded complex (Λ∗,∗(gC)∗, ∂̄) of complex valued left invariant differential forms on the nilpotent Lie group G.

A classification of Riemannian manifolds with structure group Spin (7)

SummaryRiemannian manifolds with structure group Spin (7)are 8-dimensional and have a distinguished 4 -form. In this paper, the covariant derivative of the fundamental 4 -form is studied, and it is shown that there are precisely four classes of such manifolds.

Non-Kaehler Heterotic String Compactifications with Non-Zero Fluxes and Constant Dilaton

We construct new explicit compact supersymmetric valid solutions with non-zero field strength, non-flat instanton and constant dilaton to the heterotic equations of motion in dimension six. We present balanced Hermitian structures on compact nilmanifolds in dimension six satisfying the heterotic supersymmetry equations with non-zero flux, non-flat instanton and constant dilaton which obey the three-form Bianchi identity with curvature term taken with respect to either the Levi-Civita, the (+)-connection or the Chern connection. Among them, all our solutions with respect to the (+)-connection on the compact nilmanifold M3 satisfy the heterotic equations of motion.

Compact parallelizable four-dimensional symplectic and complex manifolds

On presente des exemples de varietes symplectiques compactes sans structure complexe et/ou de structures de Kahler

Crystal Structure of Staphylococcal Enterotoxin I (SEI) in Complex with a Human Major Histocompatibility Complex Class II Molecule

Superantigens are bacterial or viral proteins that elicit massive T cell activation through simultaneous binding to major histocompatibility complex (MHC) class II and T cell receptors. This activation results in uncontrolled release of inflammatory cytokines, causing toxic shock. A remarkable property of superantigens, which distinguishes them from T cell receptors, is their ability to interact with multiple MHC class II alleles independently of MHC-bound peptide. Previous crystallographic studies have shown that staphylococcal and streptococcal superantigens belonging to the zinc family bind to a high affinity site on the class II β-chain. However, the basis for promiscuous MHC recognition by zinc-dependent superantigens is not obvious, because the β-chain is polymorphic and the MHC-bound peptide forms part of the binding interface. To understand how zinc-dependent superantigens recognize MHC, we determined the crystal structure, at 2.0Å resolution, of staphylococcal enterotoxin I bound to the human class II molecule HLA-DR1 bearing a peptide from influenza hemagglutinin. Interactions between the superantigen and DR1 β-chain are mediated by a zinc ion, and 22% of the buried surface of peptide·MHC is contributed by the peptide. Comparison of the staphylococcal enterotoxin I·peptide·DR1 structure with ones determined previously revealed that zinc-dependent superantigens achieve promiscuous binding to MHC by targeting conservatively substituted residues of the polymorphic β-chain. Additionally, these superantigens circumvent peptide specificity by engaging MHC-bound peptides at their conformationally conserved N-terminal regions while minimizing sequence-specific interactions with peptide residues to enhance cross-reactivity.

Nearly hypo structures and compact nearly Kähler 6-manifolds with conical singularities

We prove that any totally geodesic hypersurface N5 of a 6-dimensional nearly K¨ahler manifold M6 is a Sasaki–Einstein manifold, and so it has a hypo structure in the sense of Conti and Salamon [Trans. Amer. Math. Soc. 359 (2007) 5319–5343]. We show that any Sasaki–Einstein 5-manifold defines a nearly K¨ahler structure on the sin-cone N5 × R, and a compact nearly Kahler structure with conical singularities on N5 × [0, π] when N5 is compact, thus providing a link between the Calabi–Yau structure on the cone N5 × [0, π] and the nearly K¨ahler structure on the sin-cone N5 × [0, π]. We define the notion of nearly hypo structure, which leads to a general construction of nearly K¨ahler structure on N5 × R. We characterize double hypo structure as the intersection of hypo and nearly hypo structures and classify double hypo structures on 5-dimensional Lie algebras with non-zero first Betti number. An extension of the concept of nearly Kahler structure is introduced, which we refer to as nearly half-flat SU(3)-structure,and which leads us to generalize the construction of nearly parallel G2-structures on M6 × R given by Bilal and Metzger [Nuclear Phys. B 663 (2003) 343–364]. For N5 = S5 ⊂ S6 and for N5 = S2 × S3 ⊂ S3 × S3, we describe explicitly a Sasaki–Einstein hypo structure as well as the corresponding nearly K¨ahler structures on N5 × R and N5 × [0, π], and the nearly parallel G2-structures on N5 × R2 and (N5 × [0, π]) × [0, π].

Symplectic resolutions, Lefschetz property and formality

We introduce a method to resolve a symplectic orbifold (M, omega) into a smooth symplectic manifold ((M) over tilde,(omega) over tilde). Then we study how the formality and the Lefschetz property of ((M) over tilde,(omega) over tilde) are compared with that of (M, omega). We also study the formality of the symplectic blow-up of (M, omega) along symplectic submanifolds disjoint from the orbifold singularities. This allows us to construct the first example of a simply connected compact symplectic manifold of dimension 8 which satisfies the Lefschetz property but is not formal, therefore giving a counter-example to a conjecture of Babenko and Taimanov.

COMPACT SYMPLECTIC SOLVMANIFOLDS NOT ADMITTING COMPLEX STRUCTURES

In this paper the authors exhibit a family of 4-dimensional compact solvemanifolds. Each member M3(k) of the family possesses all of the topological properties of a compact Kähler manifold, yet M3(k) can have no complex structure. The proof uses Kodairas classification of compact surfaces.

Dolbeault Cohomology for G2-Manifolds

AbstractCocalibrated G2-manifolds are seven-dimensional Riemannian manifolds with a distinguished 3-form which is coclosed. For such a manifold M, S. Salamon in Riemannian Geometry and Holonomy Groups (Longman, 1989) defined a differential complex