Surgery Exact Sequence - Definition

Definition

The surgery exact sequence is defined as


\cdots \to \mathcal{N}_\partial (X \times I) \to L_{n+1} (\pi_1 (X)) \to \mathcal{S}(X) \to \mathcal{N} (X) \to L_n (\pi_1 (X))

where:

the entries and are the abelian groups of normal invariants,

the entries and are the L-groups associated to the group ring ,

the maps and are the surgery obstruction maps,

the arrows and will be explained below.

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