TY - BOOK ID - 311427 TI - Stable homotopy around the arf-kervaire invariant PY - 2009 VL - 273 SN - 1282069292 9786612069291 376439904X PB - Boston : Birkhauser, DB - UniCat KW - Homotopy theory. KW - Invariants. KW - Deformations, Continuous KW - Topology KW - Algebraic topology. KW - Algebraic Topology. UR - https://www.unicat.be/uniCat?func=search&query=sysid:311427 AB - Were I to take an iron gun, And ?re it o? towards the sun; I grant ‘twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, ‘Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n national, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, finding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 the orbit space of the free circle action S /S =CP = S . ER -