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In This Chapter
-
Moduli spaces of manifolds: a user's guide
- Introduction
- Smooth bundles and their classifying spaces
- Characteristic classes
- General versions of main results
- Stable homotopy enhancement
- MMM-classes in generalised cohomology
- General tangential structures
- Two fibre sequences
- GL d ( R ) -spaces versus spaces over BO(d)
- Boundary
- Fundamental group
- Outlook
- Rational cohomology calculations
- The manifolds W g,1
- The manifolds W g
- Hypersurfaces in CP4
- Algebraic topology of V d
- Genus of V d
- Moore–Postnikov 3-stage of V d
- Change of tangential structure
- Another Spin c (6) example
- Abelianisations of mapping class groups
- Bibliography
Abstract
The study of manifolds and invariants of manifolds was begun more than a century ago. In this entry we shall discuss the parametrised setting: invariants of families of manifolds, parametrised by a base manifold X. The invariants we look for will be cohomology classes in X, characteristic classes.
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