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An upper bound for the pseudoisotopy stable range.

Oscar Randal-Williams1

  • 1Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB UK.

Mathematische Annalen
|February 7, 2020
PubMed
Summary
This summary is machine-generated.

The pseudoisotopy stable range for 2n-dimensional manifolds has limitations, capped at a specific bound. New characteristic classes for block bundles were defined and proven non-trivial to establish this result.

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Area of Science:

  • Algebraic Topology
  • Differential Topology
  • Geometric Topology

Background:

  • The study of pseudoisotopies is crucial for understanding the topology of manifolds.
  • Previous work established connections between characteristic classes and the stable range of pseudoisotopies.

Purpose of the Study:

  • To establish a precise upper bound for the pseudoisotopy stable range of 2n-dimensional manifolds.
  • To introduce and validate new characteristic classes for block bundles.
  • To explore the rational -connectivity of certain manifolds.

Main Methods:

  • Definition and analysis of novel characteristic classes for block bundles.
  • Extension of prior theoretical frameworks on characteristic classes.
  • Application of these classes to determine the pseudoisotopy stable range.

Main Results:

  • The pseudoisotopy stable range for 2n-dimensional manifolds is proven to be no better than .
  • The non-triviality of the newly defined characteristic classes is demonstrated.
  • Rational -connectivity is established for relevant manifolds using similar techniques.

Conclusions:

  • The established bound provides a fundamental limitation on the pseudoisotopy stable range.
  • The new characteristic classes offer powerful tools for further topological investigations.
  • The results contribute to a deeper understanding of manifold structures and their properties.