Novikov-symplectic cohomology and exact Lagrangian embeddings

Let L be an exact Lagrangian submanifold inside the cotangent bundle of a closed manifold N. We prove that if N satisfies a mild homotopy assumption then the image of \pi_2(L) in \pi_2(N) has finite index. We make no assumption on the Maslov class of L, and we make no orientability assumptions. The homotopy assumption is either that N is simply connected, or more generally that \pi_m(N) is finitely generated for each m \geq 2. The result is proved by constructing the Novikov homology theory for symplectic cohomology and generalizing Viterbo's construction of a transfer map between the homologies of the free loopspaces of N and L.Comment: 27 pages; added two new sections (non-simply connected cotangent bundles, unorientable setup). The final version is published in Geometry & Topology 13, 200

Comparative actualistic study hints at origins of alleged Miocene coprolites of Poland

Excrement-shaped ferruginous masses have been recovered from the Miocene of Turów mine in south-western Poland. These siderite masses have been the subject of much controversy, having been interpreted either as being coprolites, cololithes or pseudofossils created by mechanical deformation of plastic sediment. Here we present the results of mineralogical, geochemical, petrographic and microtomographical analyses. Our data indicate that these masses consist of siderite and iron oxide rather than phosphate, and rarely contain recognizable food residues, which may suggest abiotic origins of these structures. On the other hand, evidence in support of a fecal origin include: (i) the presence of two distinct morphotypes differing in size and shape, (ii) the presence of rare hair-like structures or coalified inclusions and (iii) the presence of rare fine striations on the surface. Importantly, comparative actualistic study of recent vertebrate feces shows overall resemblance of the first morphotype (sausage-shaped with rare coalified debris) to excrements of testudinoid turtles (Testudinoidea), whose shell fragment was found in the investigated locality. The second morphotype (rounded to oval-shaped with hair-like structures), in turn, is similar to the feces of some snakes (Serpentes), the remains of which were noted in the Miocene of the neighborhood areas. Other potential producers (such as lizards and crocodiles) and even abiotic origins cannot be fully excluded but are less likely

Comparative actualistic study hints at origins of alleged Miocene coprolites of Poland

Excrement-shaped ferruginous masses have been recovered from the Miocene of Turów mine in south-western Poland. These siderite masses have been the subject of much controversy, having been interpreted either as being coprolites, cololithes or pseudofossils created by mechanical deformation of plastic sediment. Here we present the results of mineralogical, geochemical, petrographic and microtomographical analyses. Our data indicate that these masses consist of siderite and iron oxide rather than phosphate, and rarely contain recognizable food residues, which may suggest abiotic origins of these structures. On the other hand, evidence in support of a fecal origin include: (i) the presence of two distinct morphotypes differing in size and shape, (ii) the presence of rare hair-like structures or coalified inclusions and (iii) the presence of rare fine striations on the surface. Importantly, comparative actualistic study of recent vertebrate feces shows overall resemblance of the first morphotype (sausage-shaped with rare coalified debris) to excrements of testudinoid turtles (Testudinoidea), whose shell fragment was found in the investigated locality. The second morphotype (rounded to oval-shaped with hair-like structures), in turn, is similar to the feces of some snakes (Serpentes), the remains of which were noted in the Miocene of the neighborhood areas. Other potential producers (such as lizards and crocodiles) and even abiotic origins cannot be fully excluded but are less likely

Supersymmetric Configurations, Geometric Transitions and New Non-Kahler Manifolds

We give a detailed derivation of a supersymmetric configuration of wrapped D5-branes on a two-cycle of a warped resolved conifold. Our analysis reveals that the resolved conifold should support a non-Kahler metric with an SU(3) structure. We use this as a starting point of the geometric transition in type IIB theory. A mirror, and a subsequent flop transition using an intermediate M-theory configuration with a G_2 structure, gives rise to the complete IR geometric transition in type IIA theory. A further mirror transformation gives the type IIB gravity dual of the IR gauge theory on the wrapped D5-branes. Expectedly non-Kahler deformations of the resolved and the deformed conifolds appear as the gravity duals of the confining gauge theories in type IIA and type IIB theories respectively, although in more generic cases these manifolds could also be non-geometric. In the local limit we reproduce precisely the scenarios presented in our earlier works. Our present work should therefore be viewed as providing a supergravity proof of geometric transitions in the full global scenarios in type II theories.Comment: 45 pages plus appendices, 2 eps figures, LaTex JHEP3; v2: Typos corrected, some comments and references added; v3: More typos corrected and the text expanded in this final version. The version that appears in Nucl. Phys. B do not have the appendices. All the appendices in the published version are restored in this archive versio

Dipole-Deformed Bound States and Heterotic Kodaira Surfaces

We study a particular N = 1 confining gauge theory with fundamental flavors realised as seven branes in the background of wrapped five branes on a rigid two-cycle of a non-trivial global geometry. In parts of the moduli space, the five branes form bound states with the seven branes. We show that in this regime the local supergravity solution is surprisingly tractable, even though the background topology is non-trivial. New effects such as dipole deformations may be studied in detail, including the full backreactions. Performing the dipole deformations in other ways leads to different warped local geometries. In the dual heterotic picture, which is locally given by a C* fibration over a Kodaira surface, we study details of the geometry and the construction of bundles. We also point out the existence of certain exotic bundles in our framework.Comment: 40 pages, 3 .eps figures, Harvma

An Analysis of Private School Closings

We add to the small literature on private school supply by exploring exits of K-12 private schools. We find that the closure of private schools is not an infrequent event, and use national survey data from the National Center for Education Statistics to study closures of private schools. We assume that the probability of an exit is a function of excess supply of private schools over the demand, as well as the school's characteristics such as age, size, and religious affiliation. Our empirical results generally support the implications of the model. Working Paper 07-0

Geometric Transitions on non-Kaehler Manifolds

This article is based on the author's PhD--thesis. We study geometric transitions on the supergravity level using the basic idea of arXiv:hep-th/0403288, where a pair of non-Kaehler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup as suggested in arXiv:hep-th/0511099. The non-Kaehler backgrounds we obtain in type IIA are non-trivially fibered due to their construction from IIB via T-duality with Neveu-Schwarz flux. We demonstrate that these non-Kaehler manifolds are not half-flat and show that a symplectic structure exists on them at least locally. We also review the construction of new non-Kaehler backgrounds in type I and heterotic theory as proposed in arXiv:hep-th/0408192. They are found by a series of T- and S-duality and can be argued to be related by geometric transitions as well. A local toy model is provided that fulfills the flux equations of motion in IIB and the torsional relation in heterotic theory, and that is consistent with the U-duality relating both theories. For the heterotic theory we also propose a global solution that fulfills the torsional relation because it is similar to the Maldacena-Nunez background.Comment: 127 pages, based on PhD-thesis, v2 some references added, this version to appear in Fort. Phy

Comparative actualistic study hints at origins of alleged Miocene “coprolites” of Poland (supplementary movie : Tomographic animation of Miocene coprolite from Turów.avi)

Excrement-shaped siderite masseshave been the subject of much controversy. They have been variously interpreted either as being coprolites, cololithes or pseudofossils created by mechanical deformation of plastic sediment. Here we reportexcrement-shaped ferruginous masses recovered from the Miocene of Turów mine in south-western Poland. Results of mineralogical, geochemical, petrographic and microtomographical analyses indicate that these masses consist of siderite and iron oxide rather than phosphate, and rarely contain recognizable food residues, which may suggest abiotic origins of these structures. On the other hand, evidence in support of a fecal origin include: (i) the presence of two distinct morphotypes differing in size and shape, (ii) the limited quantity of specimens, (iii) the presence of rare hair-like structures or coalified inclusions and (iv) the presence of rare fine striations on the surface. Importantly, comparative actualistic study of Recent vertebrate feces shows overall resemblance of the first morphotype (sausage-shaped with rare coalified debris) to excrements of testudinoid turtles (Testudinoidea), whose shell fragment was found in the investigated locality. The second morphotype (rounded to oval-shaped with hair-like structures), in turn, is similar to the feces of some snakes (Serpentes), the remains of which were noted in the Miocene of the neighborhood areas.This research Project is partially supported by the National Science Centre, Poland (www.ncn.gov.pl), Grant No. 2019/32/C/NZ4/00150

Gauge-Gravity Dualities, Dipoles and New Non-Kahler Manifolds

In this work we explore many directions in the framework of gauge-gravity dualities. In type IIB theory we give an explicit derivation of the local metric for five branes wrapped on rigid two-cycles. Our derivation involves various interplays between warp factors, dualities and fluxes and the final result confirms our earlier predictions. We also find a novel dipole-like deformation of the background due to an inherent orientifold projection in the full global geometry. The supergravity solution for this deformation takes into account various things like the presence of a non-trivial background topology and fluxes as well as branes. Considering these, we manage to calculate the precise local solution using equations of motion. We also show that this dipole-like deformation has the desired property of decoupling the Kaluza-Klein modes from the IR gauge theory. Finally, for the heterotic theory we find new non-Kahler complex manifolds that partake in the full gauge-gravity dualities and study the mathematical structures of these manifolds including the torsion classes, Betti numbers and other topological data.Comment: Harvmac, 80 pages, 4 .eps figures; v2: Some typos corrected and new references added; v3: More typos corrected and references updated. Final version to appear in Nucl. Phys.