Steimle, Wolfgang: Obstructions to stably fibering manifolds. 2010
Inhalt
- Introduction
- Structure spaces on fibrations
- Definition of the structure space on a fibration
- Structure spaces as spaces of lifts
- Universal "bundles"
- The parametrized Whitehead torsion
- The parametrized A-theory characteristic
- Definition
- Composition rule and homeomorphism invariance
- The torsion on the stable structure space
- A product formula
- Additivity
- Relation to h-cobordisms
- Comparison with the unparametrized case
- The geometric assembly map
- Definition of the geometric assembly map
- Geometric assembly and torsion I
- Geometric assembly and torsion II
- Geometric assembly on bundles of Q-manifolds
- Whitehead torsion on Q-manifolds
- Applications to fibering questions
- Stably fibering manifolds
- Fibering Q-manifolds over compact ANRs
- Change of base and total space
- Examples I: Elementary applications
- Examples II: Stable vs. unstable fibering and TOP vs. DIFF
- A spectral sequence
- Examples III: Results of Chapman-Ferry
- Comparison with the obstructions by Farrell-Lück-Steimle
- Some results on fibrations
- The fibered homotopy extension property
- Associated fibration and connections
- Fiberwise glueing
- Glueing over different base spaces
- Tulley's construction
- Fill-in for fibrations
- Bibliography