منابع مشابه
Stable Homotopy and the J-Homomorphism
Acknowledgements I would like to thank my advisor, Prof. Michael Hopkins, for introducing me to the beautiful world of stable homotopy theory. I am grateful for the wisdom he shared, and for the time and energy he took out of a busy life to start one student down the road of curiosity and amazement. I would also like to thank my parents for their unflagging moral support, and my friends for bei...
متن کاملThe Order of the Image of the J-homomorphism
The set üS can be identified with the set of all base point preserving maps of $ into itself. SO(n)> acting on S as R with a point a t infinity, is also a set of base point preserving maps of S onto itself. This defines SO(n) C.tiS. The induced map in homotopy is called the /-homomorphism. If we allow n to go to infinity we have the stable /-homomorphism. By Bott 's results [3] 7Ty(50)=Z, i = —...
متن کاملGroup Representations, A-rings and the J-homomorphism
THIS paper arose from a desire to apply the work of J. F. Adams ‘on the groups J(X)’ [2] to the case where Xis the classifying space B, of a finite group G. Since Adams’ calculations apply only to a finite complex X, and B, is infinite, the results could not be applied directly. Rather than quoting theorems and using limiting processes, the pure algebra has been isolated and independently rewor...
متن کاملOn Whitehead Precovers
It is proved undecidable in ZFC + GCH whether every Z-module has a {Z}-precover. Let F be a class of R-modules of the form C = {A : Ext(A,C) = 0 for all C ∈ C} for some class C. The first author and Jan Trlifaj proved [7] that a sufficient condition for every module M to have an F -precover is that there is a module B such that F = {B} (= {A : Ext(B,A) = 0}). In [8], generalizing a method used ...
متن کاملOn Generalized Whitehead Products
We define a symmetric monodical pairing G ◦ H among simply connected co-H spaces G and H with the property that S(G◦H) is equivalent to the smash product G∧H as co-H spaces. We further generalize the Whitehead product map to a map G ◦ H → G ∨ H whose mapping cone is the cartesian product. Whitehead products have played an important role in unstable homotopy. They were originally introduced [Whi...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1958
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1958-10158-5