Mackey and Frobenius structures on odd dimensional surgery obstruction groups

Xianmeng Ju, Katsuhiko Matsuzaki, Masaharu Morimoto

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

C. T. C. Wall formulated surgery-obstruction groups Ln(ℤ[G] ) in terms of quadratic modules and automorphisms. C. B. Thomas showed that the Wall-group functors Ln(ℤ[-], w|_) (are modules over the Hermitian-representation-ring functor G1(ℤ-) if the orientation homomorphism w is trivial. A. Bak generalized the notion of quadratic module by introducing quadratic-form parameters, and obtained various K-groups related to quadratic modules and automorphisms. One of the authors established that some Bak groups Wn(ℤ[G], Λ; w) are equivariant-surgery- obstruction groups and showed in the case of even dimension n that the Bak-group functor Wn(ℤ[-], Λ_; w|_) is a w-Mackey functor as well as a module over the Grothendieck-Witt-ring functor GW0(ℤ,-), where w is possibly nontrivial. In this paper, we prove the same facts in the case of odd dimension n.

Original languageEnglish
Pages (from-to)285-312
Number of pages28
JournalK-Theory
Volume29
Issue number4
DOIs
Publication statusPublished - Aug 2003

Fingerprint

Frobenius
Obstruction
Surgery
Odd
Functor
Module
Automorphisms
Mackey Functor
Witt Ring
K-group
Quadratic form
Homomorphism
Equivariant
Trivial
Ring

Keywords

  • Bak group
  • Induction theory
  • Mackey functor
  • Surgery

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Mackey and Frobenius structures on odd dimensional surgery obstruction groups. / Ju, Xianmeng; Matsuzaki, Katsuhiko; Morimoto, Masaharu.

In: K-Theory, Vol. 29, No. 4, 08.2003, p. 285-312.

Research output: Contribution to journalArticle

Ju, Xianmeng ; Matsuzaki, Katsuhiko ; Morimoto, Masaharu. / Mackey and Frobenius structures on odd dimensional surgery obstruction groups. In: K-Theory. 2003 ; Vol. 29, No. 4. pp. 285-312.
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