Some calculations involving configuration spaces of distinct points
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For a manifold $X$, $\widetilde X$ denotes ''the deleted product'' of $X$, i.e. $X^2$ minus an open tubular neighborhood of the diagonal. It is a manifold with boundary and has the standard free involution. | For a manifold $X$, $\widetilde X$ denotes ''the deleted product'' of $X$, i.e. $X^2$ minus an open tubular neighborhood of the diagonal. It is a manifold with boundary and has the standard free involution. | ||
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The Haefliger-Wu invariant | The Haefliger-Wu invariant | ||
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The Haefliger-Wu invariant and the Gauss map are analogously defined for $N_0$; we will denote them by $\alpha_0$ in this case. | The Haefliger-Wu invariant and the Gauss map are analogously defined for $N_0$; we will denote them by $\alpha_0$ in this case. | ||
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Revision as of 12:55, 2 April 2020
This page has not been refereed. The information given here might be incomplete or provisional. |
Contents |
1 Introduction
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2 Construction and examples
For a manifold , denotes the deleted product of , i.e. minus an open tubular neighborhood of the diagonal. It is a manifold with boundary and has the standard free involution.
Definition 2.1.[of the Haefliger-Wu invariant ]
The Haefliger-Wu invariant is induced by the Gauss map, also denoted by . The Gauss map assigns to an individual embedding an equivariant map defined by the formula
The Haefliger-Wu invariant and the Gauss map are analogously defined for ; we will denote them by in this case.
{{{1}}} 2.2.
3 Invariants
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4 Classification/Characterization
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5 Further discussion
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