Dold manifold
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Contents |
1 Introduction
A Dold manifold is a manifold of the form
where , and the involution sends to where for .
Dold used these manifolds in [Dold1956] as generators for the unoriented bordism ring.
2 Construction and examples
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3 Invariants
Theorem [Dold1956] 3.1. The classes and generate with only the relations
and
The Steenrod squares act by
and all other Squares act trivially on and . On the decomposable classes the action is given by the Cartan formula.
The total Stiefel-Whitney class of the tangent bundle is
4 Classification/Characterization
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5 Further discussion
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6 References
- [Dold1956] A. Dold, Erzeugende der Thomschen Algebra , Math. Z. 65 (1956), 25–35. MR0079269 (18,60c) Zbl 0071.17601