2024-04-12T22:04:30Z
https://u-ryukyu.repo.nii.ac.jp/oai
oai:u-ryukyu.repo.nii.ac.jp:02007001
2022-10-31T03:13:04Z
1642837622505:1642837994858:1642837999100
1642838403551:1642838406414
Some Differentials in the mod 3 Adams Sepectral Sequence
Nakamura, Osamu
中村, 治
open access
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.
紀要論文
琉球大学理工学部
Science and Engineering Division, University of the Ryukyus
1975-03
eng
departmental bulletin paper
NA
http://hdl.handle.net/20.500.12000/23687
http://hdl.handle.net/20.500.12000/23687
https://u-ryukyu.repo.nii.ac.jp/records/2007001
AN0025080X
琉球大学理工学部紀要. 理学編
Bulletin of Science & Engineering Division, University of Ryukyus. Mathematics & natural sciences
19
1
25
https://u-ryukyu.repo.nii.ac.jp/record/2007001/files/No19p001_2.pdf
https://u-ryukyu.repo.nii.ac.jp/record/2007001/files/No19p001_1.pdf