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The Geometric Surgery Exact Sequence

  • Wolfgang Lück,
  • Tibor Macko

摘要

In this chapter we introduce the surgery exact sequence, see Theorem 11.22 and Remark 11.23. It is the realisation of the Surgery Program, which we have explained in Remark 2.9. The surgery exact sequence is the main theoretical tool in solving the classification problem of manifolds of dimensions greater than or equal to five. To get a first impression of the potential of the surgery exact sequence, we recommend studying Chapter 12. Other calculations and applications can be found in Chapters 18 and 19.