Bøger af V.V. Prasolov

Discusses the geometry and arithmetic of elliptic curves. This book includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions.

Defines simplicial homology and cohomology, with various examples and applications. This book introduces Kolmogorov-Alexander multiplication in cohomology. It deals with the applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles.

An introduction to the work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. It emphasizes the geometric aspects of the theory and discusses topics such as braids, homeomorphisms of surfaces and surgery of 3-manifolds.