The elliptic genus of Calabi-Yau 3- and 4-folds, product formulae and generalized Kac-Moody algebras

In this paper the elliptic genus for a general Calabi-Yau fourfold is derived. The recent work of Kawai calculating N=2 heterotic string one-loop threshold corrections with a Wilson line turned on is extended to a similar computation where K3 is replaced by a general Calabi-Yau 3- or 4-fold. In all cases there seems to be a generalized Kac-Moody algebra involved, whose denominator formula appears in the result.Comment: 10 pages, latex, no figure

LTA bibliography

This bibliography includes publications which deal with airship design, engineering, stress calculations, and historical information

Complete intersection singularities of splice type as universal abelian covers

It has long been known that every quasi-homogeneous normal complex surface singularity with Q-homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We describe a broad generalization: First, one has a class of complete intersection normal complex surface singularities called "splice type singularities", which generalize Brieskorn complete intersections. Second, these arise as universal abelian covers of a class of normal surface singularities with Q-homology sphere links, called "splice-quotient singularities". According to the Main Theorem, splice-quotients realize a large portion of the possible topologies of singularities with Q-homology sphere links. As quotients of complete intersections, they are necessarily Q-Gorenstein, and many Q-Gorenstein singularities with Q-homology sphere links are of this type. We conjecture that rational singularities and minimally elliptic singularities with Q-homology sphere links are splice-quotients. A recent preprint of T Okuma presents confirmation of this conjecture.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper17.abs.htm

Immersed and virtually embedded pi_1-injective surfaces in graph manifolds

We show that many 3-manifold groups have no nonabelian surface subgroups. For example, any link of an isolated complex surface singularity has this property. In fact, we determine the exact class of closed graph-manifolds which have no immersed pi_1-injective surface of negative Euler characteristic. We also determine the class of closed graph manifolds which have no finite cover containing an embedded such surface. This is a larger class. Thus, manifolds M^3 exist which have immersed pi_1-injective surfaces of negative Euler characteristic, but no such surface is virtually embedded (finitely covered by an embedded surface in some finite cover of M^3).Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-20.abs.htm

Temperature and heat flux measurements: Challenges for high temperature aerospace application

The measurement of high temperatures and the influence of heat transfer data is not strictly a problem of either the high temperatures involved or the level of the heating rates to be measured at those high temperatures. It is a problem of duration during which measurements are made and the nature of the materials in which the measurements are made. Thermal measurement techniques for each application must respect and work with the unique features of that application. Six challenges in the development of measurement technology are discussed: (1) to capture the character and localized peak values within highly nonuniform heating regions; (2) to manage large volumes of thermal instrumentation in order to efficiently derive critical information; (3) to accommodate thermal sensors into practical flight structures; (4) to broaden the capabilities of thermal survey techniques to replace discrete gages in flight and on the ground; (5) to provide supporting instrumentation conduits which connect the measurement points to the thermally controlled data acquisition system; and (6) to develop a class of 'vehicle tending' thermal sensors to assure the integrity of flight vehicles in an efficient manner