Author Archives: John Roe

About this site

  In 1996 I was the Ulam Visiting Professor at the University of Colorado, Boulder. While I was there I gave a series of graduate lectures on high-dimensional manifold theory, which I whimsically titled Surgery for Amateurs. The title was … Continue reading

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Torus trickery 201, part 2

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

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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Some TeXnicalities

Some of my students in Math 497C wanted me to divide my lecture notes into individual printouts, one for each lecture.  It is obviously a good idea to do that, but I had never tried it before because there is … Continue reading

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The Poincare sphere

Following on from my previous post, I would like to add a little introduction to the Poincare homology sphere early on in Chapter 1.  This gives an opportunity to introduce the \(E_8\) plumbing in a reasonably down-to-earth context, so it … Continue reading

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The Poincare conjecture

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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Manifolds = Bundles + Handles

The slogan in the title is one that I came up with for the book (or at least I think I did, though of course I may have stolen it from somewhere that I have now forgotten).  In my opinion … Continue reading

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Steenrod squares

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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Characteristic Classes

The next section of the book, available here, gives a very quick introduction to what the Pontrjagin classes are.  This is really just a refresher – I am sure it is too terse for someone who has never seen characteristic … Continue reading

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Manifold Sins and Wickedness

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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