Infinite loop maps and the complex $J$-homomorphism
نویسندگان
چکیده
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 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 کاملExtended flux maps on surfaces and the contracted Johnson homomorphism
On a closed symplectic surface Σ of genus two or more, we give a new construction of an extended flux map (a crossed homomorphism from the symplectomorphism group Symp(Σ) to the cohomology group H(Σ;R) that extends the flux homomorphism). This construction uses the topology of the Jacobian of the surface and a correction factor related to the Johnson homomorphism. For surfaces of genus three or...
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 کاملThe Uniqueness of Infinite Loop Space Machines
AN INFINITE loop space machine is a functor which constructs spectra out of simpler space level data. There are many such machines known[ 14,8,151. They differ somewhat in the data they accept. Worse, they are given by such widely disparate topological constructions that it is far from obvious that they turn our equivalent spectra when fed the same data. The purpose of this paper is to prove th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1976
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1976-14078-5