I am studying topology and geometry by self-study.

There are many references about algebraic topology, differential geometry, or alebraic geometry, but I think there are not so many references about differential topology. I hope there is a book of differential topology including materials about theorems about transversality, isotopy, vector bundles, etc.

I've searched in google and found some references: Milnor - Topology from the differentiable viewpoint, Guillemin&Pollack - Differential Topology, and Hirsch - Differential Topology. I've read the first book, it was good but didn't have not enough material. I've read the first chapter of the second book, this book was also good, but also I think this book doesn't have not enough material, too. I've didn't read the book of Hirsch (only the contents and it seems good) but I saw in google that people saying this book is hard for self-study and has lots of typos. This makes me unwilling to start reading this book. So I'm asking here for reference request of differential topology.

I've studied algebraic topology by Hatcher's book, and differentiable manifolds by Lee's Introduction to Smooth Manifolds, and what I'm reading now are Lee - Introduction to Riemannian Manifolds, and Bott&Tu - Differential Forms in algebraic topology. (By the way, I think the book of Bott&Tu is hard for self-study; I got stuck too many times while reading.)

Thanks in advance.


I haven't read it yet, but I think Wall's Differential Topology is the book you are looking for. Besides this one, there is also Differential Manifolds by Kosinski.


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