Relation between the Farrell-Jones conjectures in algebraic and hermitian K -theory

Naoufel Battikh[1]

  • [1] Institut préparatoire aux études d’ingénieurs de Nabeul Campus universitaire Merazka, 8000 Nabeul (Tunisie)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 1, page 197-207
  • ISSN: 0373-0956

Abstract

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We prove that if the Farrell-Jones conjecture for algebraic K -theory is true then the same conjecture for hermitian K -theory is equivalent to the fact that it exists p ∈ Z such that the assembly map is an isomorphism in degrees p and p + 1 .

How to cite

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Battikh, Naoufel. "Relation entre les conjectures de Farrell-Jones en $K$-théories algébrique et hermitienne." Annales de l’institut Fourier 57.1 (2007): 197-207. <http://eudml.org/doc/10218>.

@article{Battikh2007,
abstract = {On montre que si la conjecture de Farrell-Jones en $K$-théorie algébrique est vérifiée alors celle de la $K$-théorie hermitienne est équivalente à l’existence d’un entier $p\in Z$ tel que “assembly map” soit un isomorphisme en degré $p$ et $p+1$.},
affiliation = {Institut préparatoire aux études d’ingénieurs de Nabeul Campus universitaire Merazka, 8000 Nabeul (Tunisie)},
author = {Battikh, Naoufel},
journal = {Annales de l’institut Fourier},
keywords = {Algebraic $K$-theory; hermitian $K$-theory; Farrell-Jones conjectures},
language = {fre},
number = {1},
pages = {197-207},
publisher = {Association des Annales de l’institut Fourier},
title = {Relation entre les conjectures de Farrell-Jones en $K$-théories algébrique et hermitienne},
url = {http://eudml.org/doc/10218},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Battikh, Naoufel
TI - Relation entre les conjectures de Farrell-Jones en $K$-théories algébrique et hermitienne
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 1
SP - 197
EP - 207
AB - On montre que si la conjecture de Farrell-Jones en $K$-théorie algébrique est vérifiée alors celle de la $K$-théorie hermitienne est équivalente à l’existence d’un entier $p\in Z$ tel que “assembly map” soit un isomorphisme en degré $p$ et $p+1$.
LA - fre
KW - Algebraic $K$-theory; hermitian $K$-theory; Farrell-Jones conjectures
UR - http://eudml.org/doc/10218
ER -

References

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  1. A. Bartels, H. Reich, On the Farrell-Jones conjectures for higher algebraic K -theory, (2003) Zbl1073.19002
  2. F. T. Farrell, L. Jones, Isomorphism conjectures in algebraic K -theory, J. Amer, Math. Soc. 6 (1993), 249-297 Zbl0798.57018MR1179537
  3. A. Heller H. Bass, R. G. Swan, The whitehead group of polynomial extension, Inst. hautes études sci. 22 (1964), 61-79 Zbl0248.18026MR174605
  4. W. C. Hsiang, Borel’s conjecture, Novikov’s conjecture and the K -theoritic analogue, (1989), World scientific book, Singapour Zbl0744.57018MR1119074
  5. M. Karoubi, Le théorème fondamental de la K -théorie hermitienne, Annals of mathematics 112 (1980), 259-282 Zbl0483.18008MR592292
  6. J.-L. Loday, K -théorie algébrique et représentation de groupes, Ann. Sci. Ecole Normale Sup. Sér. 4 9 (1976), 309-377 Zbl0362.18014MR447373
  7. G. W. Whitehead, Generalised homology theories, Trans. A. M. S 102 (1962), 227-283 Zbl0124.38302MR137117

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