ON A CERTAIN SURGERY SPECTRAL SEQUENCE

A. Cavicchioli (Italy), Y. V. Muranov (Belorussia) and D. Repovš (Slovenia)

Abstract

Given a morphism between twisted quadratic extensions of antistructures, we construct a spectral sequence which generalizes, in a natural way, the surgery spectral sequence introduced by Hambleton and Kharshiladze in [Mat. Sb. 183(9) (1992), 3-14 (in Russian); English Transl. in Russian Acad. Sci. Sb. Math. 77(1) (1994), 1-9]. Our spectral sequence allows us to obtain some additional information about the Browder-Livesay invariants. Then we study the relations between the above-mentioned spectral sequences, and discuss some examples and applications.

Keywords and phrases: surgery, splitting problem, Browder-Livesay groups, Browder-Livesay invariants, spectral sequence, geometric diagram of antistructures, twisted quadratic extension.