A complement to the theory of equivariant finiteness obstructions

Paweł Andrzejewski

Fundamenta Mathematicae (1996)

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

Abstract

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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]).

How to cite

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Andrzejewski, 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

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  1. [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. [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. [3] K. Iizuka, Finiteness conditions for G-CW-complexes, Japan. J. Math. 10 (1984), 55-69. Zbl0587.57014
  4. [4] S. Kwasik, On equivariant finiteness, Compositio Math. 48 (1983), 363-372. Zbl0519.57036
  5. [5] W. Lück, The geometric finiteness obstruction, Proc. London Math. Soc. 54 (1987), 367-384. Zbl0626.57011
  6. [6] W. Lück, Transformation Groups and Algebraic K-Theory, Lecture Notes in Math. 1408, Springer, 1989. Zbl0679.57022
  7. [7] C. T. C. Wall, Finiteness conditions for CW-complexes}, Ann. of Math. 81 (1965), 55-69. Zbl0152.21902

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