Some calculations involving configuration spaces of distinct points
m (→Introduction) |
m (→Introduction) |
||
Line 15: | Line 15: | ||
== Introduction == | == Introduction == | ||
<wikitex>; | <wikitex>; | ||
− | ‘The complement of the diagonal’ and ‘the Gauss map’ ideas play a | + | ‘The complement of the diagonal’ and ‘the Gauss map’ ideas play a great role in different branches of mathematics<!-- [Gl68, Va92]-->. The Haefliger-Wu invariant is a manifestation of these ideas in the theory of embeddings. The complement to the diagonal idea originated from two celebrated theorems: the Lefschetz Fixed Point Theorem and the Borsuk-Ulam Antipodes Theorem |
</wikitex> | </wikitex> | ||
Revision as of 14:06, 2 April 2020
This page has not been refereed. The information given here might be incomplete or provisional. |
Contents |
1 Introduction
‘The complement of the diagonal’ and ‘the Gauss map’ ideas play a great role in different branches of mathematics. The Haefliger-Wu invariant is a manifestation of these ideas in the theory of embeddings. The complement to the diagonal idea originated from two celebrated theorems: the Lefschetz Fixed Point Theorem and the Borsuk-Ulam Antipodes Theorem
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
Theorem 2.2. The Haefliger-Wu invariant is one-to-one for .
3 Invariants
...
4 Classification/Characterization
...
5 Further discussion
...