On ,
Author:
Francis Clarke
Journal:
Proc. Amer. Math. Soc. 74 (1979), 156160
MSC:
Primary 55T15; Secondary 55N20
MathSciNet review:
521890
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: In this note a spectral sequence is constructed which is used to prove the existence of elements of nonzero homological degree in . Examples of specific elements in terms of representatives in the cobar construction are given.
 [1]
J.
F. Adams, Lectures on generalised cohomology, Category Theory,
Homology Theory and their Applications, III (Battelle Institute Conference,
Seattle, Wash., 1968, Vol. Three), Springer, Berlin, 1969,
pp. 1–138. MR 0251716
(40 #4943)
 [2]
J.
F. Adams, Stable homotopy and generalised homology, University
of Chicago Press, Chicago, Ill.London, 1974. Chicago Lectures in
Mathematics. MR
0402720 (53 #6534)
 [3]
, Operations of the nth kind in Ktheory, and what we don't know about , New Developments in Topology, London Math. Soc. Lecture Notes Ser., no. 11, Cambridge Univ. Press, Cambridge, 1977, pp. 19.
 [4]
Henri
Cartan and Samuel
Eilenberg, Homological algebra, Princeton University Press,
Princeton, N. J., 1956. MR 0077480
(17,1040e)
 [5]
S.
Cormack, Primitive elements in 𝐾theory, J. London
Math. Soc. (2) 9 (1974/75), 46–48. MR 0407830
(53 #11600)
 [6]
S.
P. Novikov, Methods of algebraic topology from the point of view of
cobordism theory, Izv. Akad. Nauk SSSR Ser. Mat. 31
(1967), 855–951 (Russian). MR 0221509
(36 #4561)
 [7]
Robert
M. Switzer, Algebraic topology—homotopy and homology,
SpringerVerlag, New YorkHeidelberg, 1975. Die Grundlehren der
mathematischen Wissenschaften, Band 212. MR 0385836
(52 #6695)
 [8]
Raphael
Zahler, The AdamsNovikov spectral sequence for the spheres,
Ann. of Math. (2) 96 (1972), 480–504. MR 0319197
(47 #7742)
 [1]
 J. F. Adams, Lectures on generalised cohomology, Lecture Notes in Math., vol. 99, SpringerVerlag, Berlin and New York, 1969, pp. 1138. MR 0251716 (40:4943)
 [2]
 , Stable homotopy and generalised homology, Univ. of Chicago Math. Lecture Notes, 1974. MR 0402720 (53:6534)
 [3]
 , Operations of the nth kind in Ktheory, and what we don't know about , New Developments in Topology, London Math. Soc. Lecture Notes Ser., no. 11, Cambridge Univ. Press, Cambridge, 1977, pp. 19.
 [4]
 H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N.J., 1956. MR 0077480 (17:1040e)
 [5]
 S. Cormack, Primitive elements in Ktheory, J. London Math. Soc. 9 (1974), 4648. MR 0407830 (53:11600)
 [6]
 S. P. Novikov, The methods of algebraic topology from the viewpoint of cobordism theories, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 855951 = Math. USSR Izv. 1 (1967), 827913. MR 0221509 (36:4561)
 [7]
 R. M. Switzer, Algebraic topologyhomotopy and homology, Springer, New York, 1975. MR 0385836 (52:6695)
 [8]
 R. Zahler, The AdamsNovikov spectral sequence for the spheres, Ann. of Math. (2) 96 (1972), 480504. MR 0319197 (47:7742)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC:
55T15,
55N20
Retrieve articles in all journals
with MSC:
55T15,
55N20
Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197905218907
PII:
S 00029939(1979)05218907
Keywords:
Ktheory,
unitary bordism,
Adams spectral sequence
Article copyright:
© Copyright 1979
American Mathematical Society
