Geodesic
A relative version of the finiteness obstruction theory of C. T. C. Wall
Homology, homotopy, and applications, Tome 11 (2009) no. 2, pp. 381-404.

Voir la notice de l'article provenant de la source International Press of Boston

In his 1965 paper C. T. C. Wall demonstrated that if a CW complex Y is finitely dominated, then the reduced projective class group of Y contains an obstruction which vanishes if and only if Y is homotopy equivalent to a finite CW complex. Wall also demonstrated that such an obstruction is invariant under homotopy equivalences. Subsequently Sum and Product Theorems for this obstruction were proved by L. C. Siebenmann. In his second paper on the subject Wall gives an algebraic definition of the relative finiteness obstruction. If a CW complex Y is finitely dominated rel. a subcomplex X, then the reduced projective class group of Y contains an obstruction which vanishes if and only if Y is homotopy equivalent to a finite complex rel. X. In this paper we will use a geometric construction to reduce the relative finiteness obstruction to the non-relative version. We will demonstrate that the relative finiteness obstruction is invariant under certain types of homotopy equivalences. We will also prove the relative versions of the Sum and the Product Theorems.
DOI : 10.4310/HHA.2009.v11.n2.a17
Classification : 57Q12
Keywords: CW complex, finiteness obstruction, relative finiteness obstruction 
@article{HHA_2009_11_2_a17,
     author = {Anna Davis},
     title = {A relative version of the finiteness obstruction theory of {C.} {T.} {C.} {Wall}},
     journal = {Homology, homotopy, and applications},
     pages = {381--404},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2009},
     doi = {10.4310/HHA.2009.v11.n2.a17},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n2.a17/}
}
TY  - JOUR
AU  - Anna Davis
TI  - A relative version of the finiteness obstruction theory of C. T. C. Wall
JO  - Homology, homotopy, and applications
PY  - 2009
SP  - 381
EP  - 404
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n2.a17/
DO  - 10.4310/HHA.2009.v11.n2.a17
LA  - en
ID  - HHA_2009_11_2_a17
ER  - 
%0 Journal Article
%A Anna Davis
%T A relative version of the finiteness obstruction theory of C. T. C. Wall
%J Homology, homotopy, and applications
%D 2009
%P 381-404
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n2.a17/
%R 10.4310/HHA.2009.v11.n2.a17
%G en
%F HHA_2009_11_2_a17
Anna Davis. A relative version of the finiteness obstruction theory of C. T. C. Wall. Homology, homotopy, and applications, Tome 11 (2009) no. 2, pp. 381-404. doi : 10.4310/HHA.2009.v11.n2.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n2.a17/

Cité par Sources :