Differential forms in the h-topology

Course Notes for Math 753: Differential Forms and Algebraic Topology

Modular Forms and Topology

We want to discuss various applications of modular forms in topology. The starting point is elliptic genus and its generalizations. The main techniques are the Atiyah-Singer index theorem, the Atiyah-Bott-Segal-Singer Lefschetz fixed point formula, Kac-Moody Lie algebras, modular forms and theta-functions. Just as the representations theory of classical Lie groups has close connections with the...

Differential Topology

This paper is to propose solutions to selected exercises in Differential Topology by Guillemin and Pollack, [1], and to comment on certain proofs in the book. Although the sections covered in this paper correspond to specific sections in the book, they have been freely renamed to suit the content. The sections of the book which will be covered here are, in order: §6: Homotopy and Stability Appe...

A New Topology of Embedded Z-H Buck-Boost Converter

In this paper, a new embedded Z-H (EZ-H) buck-boost converter is proposed. In this topology, two identical dc voltage sources are embedded in a LC network in a series connection with the inductors. The proposed converter eliminates the shoot-through (ST) switching state and there is no need for a front-end diode. Other advantages of the proposed topology are having capability of buck and boost ...

Differential Forms

Differentials are an important topic in algebraic geometry, allowing the use of some classical geometric arguments in the context of varieties over any field. We will use them to define the genus of a curve, and to analyze the ramification of morphisms between curves. Although differentials remain important for arbitrary varieties, we will restrict our treatment to the case of nonsingular varie...