Lectures on Principal Bundles

Comparing Lexical Bundles in Hard Science Lectures; A Case of Native and Non-Native University Lecturers

Researchers stated that learning and applying certain set of lexical bundles of native lecturers by non-native lecturers would help students improve their proficiency through incidental vocabulary input. The present study shed light on the lexical bundles in hard science lectures used by Native and Non-native lecturers in international universities with the main purpose of analyzing the structu...

A COVERING PROPERTY IN PRINCIPAL BUNDLES

Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

Lectures On Fibre Bundles and Di ff erential Geometry

Lectures on Algebro-geometric Chern-weil and Cheeger-chern-simons Theory for Vector Bundles

Lectures on Noncommutative Geometry

These Lectures are based on a course on noncommutative geometry given by the author in 2003. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild cohomology, Serre functors, etc. We also discuss many less known as well as some new results such as noncommutative Chern-Weil theory, noncommutative symplectic geometry, noncommutative diffe...