FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 3, PAGES 797-828

L-theory for local systems of homotopy coalgebras and the exact sequence for surgery

S. V. Lapin

Abstract

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In this work various versions of L-theory for local systems of homotopy coalgebras over simplicial complexes are developed. The relation to L-theory for local systems of chain complexes is examined. We give a construction of $$W-spectra whose homotopy groups are equal to the corresponding bordism groups of local systems of homotopy Poincare coalgebras. By means of these $$W-spectra the exact sequence for surgery in L-theory for homotopy coalgebras is obtained.

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Last modified: December 23, 2001