I am just about to finish my study of Milnor's book 'Topology from the Differentiable Viewpoint' and I really love the subject. I would like to continue my study of Differential Topology and am looking for some good references. What are the canonical choices of textbooks for this subject ? I am a...
In Milnor's book "Topology from the Differentiable Viewpoint", He states the following lemma: Let $M, N$ be oriented $n$ manifolds, with $M$ compact and $N$ connected. Let $f : M \to N$ be a smooth map, and $y$ a regular value of $f$. Also, suppose $f$ can be extended to $F : X \to N$ where X is...
Milnor's 'Lectures on h-cobordism theorem' Theorem 7.6 ("Basis Theorem") reads Suppose $(W;V,V')$ is a triad of dimension $n$ (ie. a cobordism $W$ between $V$ and $V'$) possessing a Morse function $f$ with all critical points of index $\lambda$ and on the same level, and let $\xi$ be a gradie...
I'am trying to come up with a solution to the referred problem which, by the way, states the following: If $m<p$, show that every map $M^m\to S^p$ is homotopic to a constant map. From the chapter, you may (must) assume $M$ is a compact (and, may be, boundaryless) smooth ($=C^\infty$) manifold (...
What are the (exact sentence of) Unreadable lines of the following images of Milnor's Lecture on h-cobordism theorem? (pages number: 28, 30, 15 respectively)
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