Algebraic glueing

Geometric Poincare cobordisms (VjX.X ). (V, X, X ) can be glued together to define a geometric Poincare cobordism (Y X,X ) with 

We shall now recall from 1.3 the analogue of this glueing operation for algebraic Poincar4 cobordisms. 

The union operation for algebraic Poincare cobocdisms hs a particularly simple expression (up to hoinotopy equivalence) in the special case when all the chain maps involved are defir by Inclusions of direct summands, as follows. 

The direct union of adjoining direct (n+1)-dimensional e-symmetric c-quadratic c = ( (f f C C - 

Furthermore, if c,c are adjoining algebraic Poincare cobordisms there is defined a homotopy equivalence cue - c uc  

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We have the following algebraic version of the Novikov additivity property for the signature, involving the glueing of forms defined in 1.7. 

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