# A complement to the theory of equivariant finiteness obstructions

Fundamenta Mathematicae (1996)

- Volume: 151, Issue: 2, page 97-106
- ISSN: 0016-2736

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topAndrzejewski, Paweł. "A complement to the theory of equivariant finiteness obstructions." Fundamenta Mathematicae 151.2 (1996): 97-106. <http://eudml.org/doc/212191>.

@article{Andrzejewski1996,

abstract = {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 $K_0(ℤ [π_0(WH(X))_α^*])$. We prove that every family $\{w_α^H\}$ of elements of the groups $K_0(ℤ [π_0(WH(X))_α^*])$ can be realized as the family of equivariant finiteness obstructions $w^H_α(X)$ 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]).},

author = {Andrzejewski, Paweł},

journal = {Fundamenta Mathematicae},

keywords = {finiteness obstruction},

language = {eng},

number = {2},

pages = {97-106},

title = {A complement to the theory of equivariant finiteness obstructions},

url = {http://eudml.org/doc/212191},

volume = {151},

year = {1996},

}

TY - JOUR

AU - Andrzejewski, Paweł

TI - A complement to the theory of equivariant finiteness obstructions

JO - Fundamenta Mathematicae

PY - 1996

VL - 151

IS - 2

SP - 97

EP - 106

AB - 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 $K_0(ℤ [π_0(WH(X))_α^*])$. We prove that every family ${w_α^H}$ of elements of the groups $K_0(ℤ [π_0(WH(X))_α^*])$ can be realized as the family of equivariant finiteness obstructions $w^H_α(X)$ 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]).

LA - eng

KW - finiteness obstruction

UR - http://eudml.org/doc/212191

ER -

## References

top- [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.
- [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. Zbl0741.57012
- [3] K. Iizuka, Finiteness conditions for G-CW-complexes, Japan. J. Math. 10 (1984), 55-69. Zbl0587.57014
- [4] S. Kwasik, On equivariant finiteness, Compositio Math. 48 (1983), 363-372. Zbl0519.57036
- [5] W. Lück, The geometric finiteness obstruction, Proc. London Math. Soc. 54 (1987), 367-384. Zbl0626.57011
- [6] W. Lück, Transformation Groups and Algebraic K-Theory, Lecture Notes in Math. 1408, Springer, 1989. Zbl0679.57022
- [7] C. T. C. Wall, Finiteness conditions for CW-complexes}, Ann. of Math. 81 (1965), 55-69. Zbl0152.21902

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