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Monthly Archives: August 2013
The Poincare conjecture
The next few sections of Chapter 1 are intended to introduce some key examples of constructions with manifolds: The highdimensional Poincaré conjecture and the hcobordism theorem Milnor’s exotic spheres Variation of Pontrjagin classes within a homotopy type In the version … Continue reading
Posted in Discussion, math
Tagged cobordism, exotic sphere, Poincare conjecture, Poincare duality
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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
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
Posted in Discussion, math
Tagged characteristic class, cohomology, Steenrod squares
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