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No.19 (1975/03) >

 
Title :Some Differentials in the mod 3 Adams Sepectral Sequence
Authors :Nakamura, Osamu
Authors alternative :中村, 治
Issue Date :Mar-1975
Abstract :Let A_p be the mod p Steenrod algebra. J. F. Adams [1] introduced a spectral sequence which has as its E_2 term Ext_A_p (H*(X), Z_p) and which converges to a graded algebra associated to π^s_*(X;p) i. e., the p-primary stable homotopy groups of X. In this paper we will study this sequence for X=S^n, P=3. The first problem in any use of the Adams spectral sequence is to obtain E_2 = Ext^<s,t>_<A_3>(Z_3, Z_3). We do this by the technique of J. P. May [5] J. P. May constructed another spectral sequence which has as its E_∞ term an algebra E^oExt, i. e. a tri-graded algebra associated to E_2 = Ext. In [9], we extended (and corrected) May's computations to obtain complete information on E_oExt through dimension 158. The next problem is to obtain the differentials in the Adams spectral sequence. J. P. May [5] and S.Oka have previously determined all differentials at least in the range t-s≦77 by using the results of the 3-components of stable homotopy groups of sphere which have been calculated by H.Toda [12,13,14,15] J.P.May [5] and S.Oka [10]. The purpose of this paper is to evaluate the differentials in the range 78≦t-s≦104. Our main result is Theorem 3.19. Finally the auther wishes to extend his gratitude to Dr. Shichiro Oka for valuable information and discussions during this investigation.
Type Local :紀要論文
Publisher :琉球大学理工学部
URI :http://hdl.handle.net/20.500.12000/23687
Citation :琉球大学理工学部紀要. 理学編 = Bulletin of Science & Engineering Division, University of Ryukyus. Mathematics & natural sciences no.19 p.1 -25
Appears in Collections:No.19 (1975/03)

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