Some results on vector bundle monomorphisms

In this paper we use the singularity method of Koschorke [2] to study the question of how many different nonstable homotopy classes of monomorphisms of vector bundles lie in a stable class and the percentage of stable monomorphisms which are not homotopic to stabilized nonstable monomorphisms. Particular attention is paid to tangent vector fields. This work complements some results of Koschorke [3; 4], Libardi-Rossini [7] and Libardi-do Nascimento-Rossini [6].

On The Brill-noether Theory of Spanned Vector Bundles on Smooth Curves

Here we study the integers (d, g, r) such that on a smooth projective curve of genus g there exists a rank r stable vector bundle with degree d and spanned by its global sections.

Remarks on the normal bordism forgetful homomorphism

Assume that X is an oriented smooth (n+k)-manifold. Then the kernel of the forgetful map F considered in this work consists of immersions f: Mn → X nullbordant as a continuous map. Using an exact sequence of normal bordism groups previously given, we present a homological characterization of the kernel of the forgetful map F. Also, we prove that Ωi(X, εs - ηs and Hi(X,Z) are -isomorphic for i≤3 and C2-isomorphic for i≤2, where C2,3 (resp. C2 is the class of abelian groups whose elements have order 2p. 3q (resp. 2p), and ηs is an orientable stable vector bundle over X. © 2009 Pushpa Publishing House.

l-stable Functions and Constrained Optimization

Иван Гинчев - Класът на ℓ-устойчивите в точка функции, дефиниран в [2] и разширяващ класа на C1,1 функциите, се обобщава от скаларни за векторни функции. Доказани са някои свойства на ℓ-устойчивите векторни функции. Показано е, че векторни оптимизационни задачи с ограничения допускат условия от втори ред изразени чрез посочни производни, което обобщава резултати от [2] и [5].

Heat flow for Yang-Mills-Higgs fields, part I

The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.

Heat flow for the Yang-Mills-Higgs field and the Hermitian Yang-Mills-Higgs metric

For a parameter lambda > 0, we study a type of vortex equations, which generalize the well-known Hermitian-Einstein equation, for a connection A and a section phi of a holomorphic vector bundle E over a Kahler manifold X. We establish a global existence of smooth solutions to heat flow for a self-dual Yang-Mills-Higgs field on E. Assuming the lambda -stability of (E, phi), we prove the existence of the Hermitian Yang-Mills-Higgs metric on the holomorphic bundle E by studying the limiting behaviour of the gauge flow.

Clonal Relationship among Atypical Enteropathogenic Escherichia coli Strains Isolated from Different Animal Species and Humans

Forty-nine typical and atypical enteropathogenic Escherichia coli (EPEC) strains belonging to different serotypes and isolated from humans, pets (cats and dogs), farm animals (bovines, sheep, and rabbits), and wild animals (monkeys) were investigated for virulence markers and clonal similarity by pulsed-field gel electrophoresis (PFGE) and multilocus sequence typing (MLST). The virulence markers analyzed revealed that atypical EPEC strains isolated from animals have the potential to cause diarrhea in humans. A close clonal relationship between human and animal isolates was found by MLST and PFGE. These results indicate that these animals act as atypical EPEC reservoirs and may represent sources of infection for humans. Since humans also act as a reservoir of atypical EPEC strains, the cycle of mutual infection of atypical EPEC between animals and humans, mainly pets and their owners, cannot be ruled out since the transmission dynamics between the reservoirs are not yet clearly understood.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

Remarks on immersions in the metastable dimension range

In this work we present a generalization of an exact sequence of normal bordism groups given in a paper by H. A. Salomonsen (Math. Scand. 32 (1973), 87-111). This is applied to prove that if h : M-n --> Xn+k, 5 less than or equal to n < 2k, is a continuous map between two manifolds and g : M-n --> BO is the classifying map of the stable normal bundle of h such that (h, g)(*) : H-i (M, Z(2)) --> H-i (X x BO, Z(2)) is an isomorphism for i < n - k and an epimorphism for i = n - k, then h bordant to an immersion implies that h is homotopic to an immersion. The second remark complements the result of C. Biasi, D. L. Goncalves and A. K. M. Libardi (Topology Applic. 116 (2001), 293-303) and it concerns conditions for which there exist immersions in the metastable dimension range. Some applications and examples for the main results are also given.

Development of HIV vectors for anti-HIV gene therapy.

Current gene therapy protocols for HIV infection use transfection or murine retrovirus mediated transfer of antiviral genes into CD4+ T cells or CD34+ progenitor cells ex vivo, followed by infusion of the gene altered cells into autologous or syngeneic/allogeneic recipients. While these studies are essential for safety and feasibility testing, several limitations remain: long-term reconstitution of the immune system is not effected for lack of access to the macrophage reservoir or the pluripotent stem cell population, which is usually quiescent, and ex vivo manipulation of the target cells will be too expensive and impractical for global application. In these regards, the lentivirus-specific biologic properties of the HIVs, which underlie their pathogenetic mechanisms, are also advantageous as vectors for gene therapy. The ability of HIV to specifically target CD4+ cells, as well as non-cycling cells, makes it a promising candidate for in vivo gene transfer vector on one hand, and for transduction of non-cycling stem cells on the other. Here we report the use of replication-defective vectors and stable vector packaging cell lines derived from both HIV-1 and HIV-2. Both HIV envelopes and vesicular stomatitis virus glycoprotein G were effective in mediating high-titer gene transfer, and an HIV-2 vector could be cross-packaged by HIV-1. Both HIV-1 and HIV-2 vectors were able to transduce primary human macrophages, a property not shared by murine retroviruses. Vesicular stomatitis virus glycoprotein G-pseudotyped HIV vectors have the potential to mediate gene transfer into non-cycling hematopoietic stem cells. If so, HIV or other lentivirus-based vectors will have applications beyond HIV infection.

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.

Sasakian quiver gauge theories and instantons on cones over lens 5-spaces

We consider SU(3)-equivariant dimensional reduction of Yang Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3)-equivariant solutions to the Hermitian Yang-Mills equations on the associated Calabi-Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as Kahler quotients and show that they have the same cyclic orbifold singularities as the cones over the lens 5-spaces. (C) 2015 The Authors. Published by Elsevier B.V.

Immersions of Manifolds

Immersions of an m-manifold in an n-manifold, n>m, are classified up to regular homotopy by the homotopy classes of sections of a vector bundle E associated to the tangent bundle of M.  When N = Rn , the fibre of E is the Stiefel manifold of m-frames in n-space.

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)