Algebraic topology from geometric viewpoint

TL;DR

This book introduces core concepts of algebraic topology through geometric problems, making the subject accessible with minimal technical details for readers with basic topology knowledge.

Contribution

It presents algebraic topology ideas in a geometric context, bridging applications and theory with minimal technical complexity.

Findings

Main notions like homology groups and characteristic classes are derived from geometric problems.

Accessible to undergraduates and non-specialists, promoting broader understanding.

Provides a minimal-technical exposition suitable for educational and casual reading.

Abstract

This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and invariants, characteristic classes). Thus main ideas of algebraic topology are presented with minimal technicalities. Familiarity of a reader with basic notions of topology (such as 2-dimensional manifolds and vector fields) is desirable, although definitions are given at the beginning. The book is accessible to undergraduates and could also be an interesting easy reading for professional mathematicians.