Category Archives: Discussion

Torus trickery 201, part 2

Posted on January 11, 2014 by John Roe

So how are appropriate versions of Facts 1 and 2 (from the previous post) to be proved, and what has this all got to do with the torus? The Euclidean space \({\mathbb R}^2\) that appears is a little piece of … Continue reading →

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Torus trickery 201

Posted on January 3, 2014 by John Roe

One of the things I really want to do with the Surgery for Amateurs project is to make a reasonably plausible presentation of surgery theory for topological manifolds, as well as for smooth and/or PL.  But this requires one to … Continue reading →

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The Poincare conjecture

Posted on August 29, 2013 by John Roe

The next few sections of Chapter 1 are intended to introduce some key examples of constructions with manifolds: The high-dimensional Poincaré conjecture and the h-cobordism theorem Milnor’s exotic spheres Variation of Pontrjagin classes within a homotopy type In the version … Continue reading →

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Steenrod squares

Posted on August 21, 2013 by John Roe

The Steenrod squares are discussed at some length in Chapter 5 of the book (so we’re getting a bit out of sequence here).  But they are also, of course, closely related to characteristic classes: Milnor and Stasheff’s book defines the … Continue reading →

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Manifold Sins and Wickedness

Posted on July 9, 2013 by John Roe

In the previous post I mentioned the two categories of manifolds with which we’re going to be mostly concerned: smooth manifolds, equipped with an atlas whose transition maps are \(C^\infty\), and topological manifolds (locally Euclidean spaces).  Smooth manifolds are, of … Continue reading →

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