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Algebraic surgery

Proposition 1.5.1 i) Algebraic surgery preserves the homotopy type of the boundary. In particular, surgery on an algebraic Poincare complex results in an algebraic Poincare complex, ii) Algebraic Poincarl complexes x,y are cobordant if and only if X is homotopy equivalent to a complex obtained from y by surgery. [Pg.59]

The criterion of Proposition 1.5.2 for the skew-suspension map to be an isomorphism is always satisfied in the e-quadratic ca cf. Proposition 1.2,2 i). It is not in general satisfied in th e-symmetric case, cf. Proposition 1.2.2 li) and the examples o non-periodic e-symmetric L-groups of SI.10. [Pg.59]


Proof See Propositions I.4.3,I.4.5. (The proofs use the algebraic surgery technique summarized in Sl 5 below). [Pg.39]

See Proposition 7.1.4 (rel3) iv) below for the algebraic surgery exact sequence involving S" (X), and for an expression of the difference slf. f ) as a rel3 s-triangulability obstruction). Proof See Ranicki (7. ... [Pg.557]

Proposition 7.3.5 A geometric surgery on a formally n-dlmenslonal topological normal map (f,h) M-- X determines an algebraic surgery on the quadratic kernel o,(f,b). [Pg.605]

I should like to thank Jean Lannes for his suggestion that I apply the algebraic theory of surgery to normal maps which bound as degree 1 maps) ... [Pg.142]

We shall now use algebraic Poincare surgery and the spectral quadratic construction to define quadratic signature maps... [Pg.618]

There is a corresponding algebraic notion of ambient surgery on a pair of the type... [Pg.653]

The algebraic effect Is an ambient surgery on the quadratic kernel pair... [Pg.656]

From the point of view of the algebraic theory of codimension 1 surgery the above decompositions of the elements sGL (A x,x 1,E) may be deduced from the following... [Pg.744]

An algebraic formulation of surgery Trinity College fellowship dissertation (197 Localization in quadratic L-theory... [Pg.856]

Splitting theorems in the algebraic theory of surgery in preparation [12] Classifying spaces in the algebraic theory of surgery in preparation... [Pg.857]

In Parts 1 and II of a paper entitled "The algebraic theory of surgery" (Ranicki (9I, 10, henceforth to be denoted I.,II.) the cobordism of algebraic Poincare complexes r syroroetr ic... [Pg.869]


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