Poles, zeros, and sheaf cohomology

Generalised sheaf cohomology theories

This paper is an expanded version of notes for a set of lectures given at the Isaac Newton Institute for Mathematical Sciences during a NATO ASI Workshop entitled “Homotopy Theory of Geometric Categories” on September 23 and 24, 2002. This workshop was part of a program entitled New Contexts in Stable Homotopy Theory that was held at the Institute during the fall of 2002. The intent for the lec...

Ordinary and Generalized Sheaf Cohomology

This article is expanded from a talk given by the author in (the preliminary version of) the Student Algebraic Topology seminar in University of Michigan, Ann Arbor. The rst part will be a review of ordinary sheaf cohomology which is done in such a way that generalization to generalized sheaf cohomology theory becomes automatic. The second part is a quick introduction of the approach to general...

Sheaf Cohomology of Conscious Entity

Awareness of a conscious entity can exist without elements; therefore, the general notion of an object of a category is employed. One of the characterization of understanding is: for a given local infonnation (awareness) there exists a global information whose restriction is the given information. For such mental activities, category and sheaf theories are employed to formulate consciousness. W...

A Gentle Introduction to Homology, Cohomology, and Sheaf Cohomology

Sheaf Cohomology, and the Heterotic Standard Model

Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequen...