Lectures In Geometry Semester 3 Volume 1 Smooth Manifolds | M. Postnikov

This book is actually Semester 3 of my Lectures in Geometry. It starts a new subject, however, and is there­ fore independent of the previous two semesters.

The book has two major features that distinguish it from other textbooks on elementary smooth manifold the­ ory. Firstly, a lot of space is allotted to topological dimensional theory, the most geometry-oriented branch of general topology, and an acquaintance with it will bring joy to lovers of elegant mathematical constructions which provide deep insights. Secondly, I’ve ventured, in this elementary course, to present the basic notions of the theory of spectral sequences, a tool whose power

and significance is becoming increasingly clear in current studies. This is done without first expounding general (co)homology theory .