The Collar Theorem

  • Daniel S. Freed
  • Karen K. Uhlenbeck
  • Mathematical Sciences Research Institute
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 1)

Abstract

We complete the proof of Donaldson’s Theorem in this chapter by showing that for ⋋ sufficiently small,
\( M\lambda = \{ \overline D \in M:\lambda \left( {\overline D } \right) \leqslant \lambda \} \) is diffeomorphic to (0, ⋋) x M. Recall from (8.30) that for ⋋ ≤ ⋋4 there is a well-defined smooth map
$$ \overline B :{M_{\lambda }} \to (0,\lambda ) \times M\overline D \mapsto \langle \lambda (\overline D ),x(\overline D )\rangle . $$

Keywords

Manifold Expense 

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Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Daniel S. Freed
    • 1
  • Karen K. Uhlenbeck
    • 1
  • Mathematical Sciences Research Institute
    • 2
  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA
  2. 2.BerkeleyUSA

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