A complement to the theory of equivariant finiteness obstructions

Andrzejewski, Paweł

Fundamenta Mathematicae, Tome 149 (1996), p. 97-106 / Harvested from The Polish Digital Mathematics Library

Résumé

It is known ([1], [2]) that a construction of equivariant finiteness obstructions leads to a family $w_{α}^{H} (X)$ of elements of the groups $K_{0} (ℤ [π_{0} {(W H (X))}_{α}^{*}])$ . We prove that every family $w_{α}^{H}$ of elements of the groups $K_{0} (ℤ [π_{0} {(W H (X))}_{α}^{*}])$ can be realized as the family of equivariant finiteness obstructions $w_{α}^{H} (X)$ of an appropriate finitely dominated G-complex X. As an application of this result we show the natural equivalence of the geometric construction of equivariant finiteness obstruction ([5], [6]) and equivariant generalization of Wall’s obstruction ([1], [2]).

Publié le : 1996-01-01

Zbl 0882.57018

EUDML-ID : urn:eudml:doc:212191

@article{bwmeta1.element.bwnjournal-article-fmv151i2p97bwm,
     author = {Pawe\l\ Andrzejewski},
     title = {A complement to the theory of equivariant finiteness obstructions},
     journal = {Fundamenta Mathematicae},
     volume = {149},
     year = {1996},
     pages = {97-106},
     zbl = {0882.57018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv151i2p97bwm}
}

Andrzejewski, Paweł. A complement to the theory of equivariant finiteness obstructions. Fundamenta Mathematicae, Tome 149 (1996) pp. 97-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv151i2p97bwm/

Bibliographie

[00000] [1] P. Andrzejewski, The equivariant Wall finiteness obstruction and Whitehead torsion, in: Transformation Groups, Poznań 1985, Lecture Notes in Math. 1217, Springer, 1986, 11-25.

[00001] [2] P. Andrzejewski, Equivariant finiteness obstruction and its geometric applications - a survey, in: Algebraic Topology, Poznań 1989, Lecture Notes in Math. 1474, Springer, 1991, 20-37. | Zbl 0741.57012

[00002] [3] K. Iizuka, Finiteness conditions for G-CW-complexes, Japan. J. Math. 10 (1984), 55-69. | Zbl 0587.57014

[00003] [4] S. Kwasik, On equivariant finiteness, Compositio Math. 48 (1983), 363-372. | Zbl 0519.57036

[00004] [5] W. Lück, The geometric finiteness obstruction, Proc. London Math. Soc. 54 (1987), 367-384. | Zbl 0626.57011

[00005] [6] W. Lück, Transformation Groups and Algebraic K-Theory, Lecture Notes in Math. 1408, Springer, 1989. | Zbl 0679.57022

[00006] [7] C. T. C. Wall, Finiteness conditions for CW-complexes}, Ann. of Math. 81 (1965), 55-69. | Zbl 0152.21902