转自：http://www.map.mpim-bonn.mpg.de/Manifolds_with_singularities

Manifolds with singularities

This page has not been refereed. The information given here might be incomplete or provisional.

Contents

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• 1 Introduction
• 2 Definitions
  • 2.1 Cone-like singularities
  • 2.2 \Sigma-manifolds
• 3 Some examples and constructions
  • 3.1 Intersecting spheres
  • 3.2 Inverse images of critical points
  • 3.3 Structures on manifolds with singularities
  • 3.4 Bundles on manifolds with singularities
• 4 Bordism theory for manifolds with singularities
• 5 Invariants
• 6 Classification/Characterization
• 7 Further discussion
• 8 References

[edit]1 Introduction

Manifolds with singularities are geometric objects in topology generalizing manifolds. They were introduced 

in ([Sullivan1996],[Sullivan1967]) and [Baas1973]. Applications of the concept include representing cycles in 

homology theories with coefficients. All manifolds in this article are understood to be smooth.

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