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)
The idea of creating a tag concerning a specific author seem to be even worse then a tag on a specific text. All the objections in the linked meta posts above still applies, and such a tag provides very little information. (Think of a tag about Serge Lang or Bourbaki for example)
I have checked which users were adding the elementary-probability tag. If there were some rather experienced users among them, it might be useful to consult them before removal.
@Did Since you are among the users who are active in probability-related tags and you were also active in some tag-related discussions on meta, I wanted to make sure that you know about the plans to remove the elementary-probability tag (to be more precise, to merge it into probability).
Following an earlier discussion I approved a synonym elementary-probability to probability. Likely down the road a merge will happen.
The main reasons are:
we do not separate tags by level, and in this case there even is probability-theory that is an "advanced" tag so that further separation...
The tag description:
The Pochhammer symbol is the notation used for rising and falling factorials. The $q$-Pochhammer symbol is the $q$-analog.
To be a $q$-analog, the $q$-Pochhammer symbol must equal the original expression (rising or falling factorial) as $q \rightarrow 1$ (or at least $q...
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)
Following an earlier discussion I approved a synonym elementary-probability to probability. Likely down the road a merge will happen.
The main reasons are:
we do not separate tags by level, and in this case there even is probability-theory that is an "advanced" tag so that further separation...
The tag description:
The Pochhammer symbol is the notation used for rising and falling factorials. The $q$-Pochhammer symbol is the $q$-analog.
To be a $q$-analog, the $q$-Pochhammer symbol must equal the original expression (rising or falling factorial) as $q \rightarrow 1$ (or at least $q...
