The Goodwillie tower for S[superscript 1] and Kuhn's Theorem
نویسندگان
چکیده
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We analyze the homological behavior of the attaching maps in the 2-local Good-willie tower of the identity evaluated at S 1. We show that they exhibit the same homological behavior as the James-Hopf maps used by N. Kuhn to prove the 2-primary Whitehead conjecture. We use this to prove a calculus form of the Whitehead conjecture: the Whitehead sequence is a contracting homotopy for the Goodwillie tower of S 1 at the prime 2.
منابع مشابه
The Goodwillie tower for S1 and Kuhn’s theorem
We analyze the homological behavior of the attaching maps in the 2-local Goodwillie tower of the identity evaluated at S1 . We show that they exhibit the same homological behavior as the James-Hopf maps used by N. Kuhn to prove the 2-primary Whitehead conjecture. We use this to prove a calculus form of the Whitehead conjecture: the Whitehead sequence is a contracting homotopy for the Goodwillie...
متن کاملAlgebraic Goodwillie Calculus and a Cotriple Model for the Remainder
We define an “algebraic” version of the Goodwillie tower, P alg n F (X), that depends only on the behavior of F on coproducts of X . When F is a functor to connected spaces or grouplike H-spaces, the functor P alg n F is the base of a fibration |⊥ F | → F → P alg n F, whose fiber is the simplicial space associated to a cotriple ⊥ built from the (n + 1) cross effect of the functor F . When the c...
متن کاملTopological Nonrealization Results via the Goodwillie Tower Approach to Iterated Loopspace Homology
We prove a strengthened version of a theorem of Lionel Schwartz that says that certain modules over the Steenrod algebra cannot be the mod 2 cohomology of a space. What is most interesting is our method, which replaces his iterated use of the Eilenberg–Moore spectral sequence by a single use of the spectral sequence converging to H(ΩX;Z/2) obtained from the Goodwillie tower for ΣΩX. Much of the...
متن کاملThe Goodwillie tower and the EHP sequence
We study the interaction between the EHP sequence and the Goodwillie tower of the identity evaluated at spheres at the prime 2. Both give rise to spectral sequences (the EHP spectral sequence and the Goodwillie spectral sequence, respectively) which compute the unstable homotopy groups of spheres. We relate the Goodwillie filtration to the P map, and the Goodwillie differentials to the H map. F...
متن کاملar X iv : 0 70 9 . 39 25 v 2 [ m at h . A T ] 3 D ec 2 00 7 HOMOTOPY NILPOTENT GROUPS
We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove, that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups and that ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011