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), 473-487

MSC (2000):
Primary 55P47, 55Q45, 55S10, 55T15

DOI:
https://doi.org/10.1090/S0002-9947-04-03661-X

Published electronically:
May 28, 2004

MathSciNet review:
2095619

Full-text PDF

Abstract | References | Similar Articles | 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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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:
Minh-Ha.Le@math.univ-lille1.fr

**Nguyên H. V. Hung**

Affiliation:
Department of Mathematics, Vietnam National University, 334 Nguyên Trãi Street, Hanoi, Vietnam

Email:
nhvhung@vnu.edu.vn

DOI:
https://doi.org/10.1090/S0002-9947-04-03661-X

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 DMS-0079743

Dedicated:
Dedicated to Professor Huỳnh Mùi on the occasion of his sixtieth birthday

Article copyright:
© Copyright 2004
American Mathematical Society