An attack on the Kervaire invariant conjecture
The present thesis developed in three stages, each associated with a particular problem. The problems are, in 'historical' order: (1) (The Kervaire invariant problem): Find out for which positive integers k the Kervaire invariant Φ:πs2k -> z2 is onto. (2) Given a fibration f:B -> BO, with associated Thom spectrum M(B, f) [STONG], is there any useful connection between the surgery obstruction group L2k(π1(B), π1(f)) on one hand and the bordism group π2k(M(B,f)) on the other? (3) Construct a general theory of signature invariants which will please the handlebody theorist. Of course (2) and (3) are just means of escaping from (1).