On the behavior of the algebraic transfer
Authors:
Robert R. Bruner, Lê M. Hà and Nguyên H. V. Hung
Journal:
Trans. Amer. Math. Soc. 357 (2005), 473487
MSC (2000):
Primary 55P47, 55Q45, 55S10, 55T15
Published electronically:
May 28, 2004
MathSciNet review:
2095619
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: Let be the algebraic transfer, which is defined by W. Singer as an algebraic version of the geometrical transfer . It has been shown that the algebraic transfer is highly nontrivial and, more precisely, that is an isomorphism for . However, Singer showed that is not an epimorphism. In this paper, we prove that does not detect the nonzero element for every . As a consequence, the localized given by inverting the squaring operation is not an epimorphism. This gives a negative answer to a prediction by Minami.
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 M. Kameko, Products of projective spaces as Steenrod modules, Thesis, Johns Hopkins University 1990.
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 M. Kameko, Generators of the cohomology of , J. Math. Kyoto Univ. 38 (1998), 587593. MR 2000b:55015
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Additional Information
Robert R. Bruner
Affiliation:
Department of Mathematics, Wayne State University, 656 W. Kirby Street, Detroit, Michigan 48202
Email:
rrb@math.wayne.edu
Lê M. Hà
Affiliation:
Université de Lille I, UFR de Mathématiques, UMR 8524, 59655 Villeneuve d’Ascq Cédex, France
Email:
MinhHa.Le@math.univlille1.fr
Nguyên H. V. Hung
Affiliation:
Department of Mathematics, Vietnam National University, 334 Nguyên Trãi Street, Hanoi, Vietnam
Email:
nhvhung@vnu.edu.vn
DOI:
http://dx.doi.org/10.1090/S000299470403661X
PII:
S 00029947(04)03661X
Keywords:
Adams spectral sequences,
Steenrod algebra,
invariant theory,
algebraic transfer
Received by editor(s):
June 18, 2003
Published electronically:
May 28, 2004
Additional Notes:
The third author was supported in part by the Vietnam National Research Program, Grant N$^{0} 140 801$. The computer calculations herein were done on equipment supplied by NSF grant DMS0079743
Dedicated:
Dedicated to Professor Huỳnh Mùi on the occasion of his sixtieth birthday
Article copyright:
© Copyright 2004
American Mathematical Society
