Geodesic
Arithmetic Invariants of Subdivision of Complexes
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 92-96

Voir la notice de l'article provenant de la source Cambridge University Press

The following problem was raised by M. Brown. Let K be a finite simplicial complex, of dimension n, with αi(K) simplexes of dimension i. Which of the linear combinations have the property that they are unaltered by all stellar subdivisions of K? The most obvious invariant is the Euler characteristic; there are also some identities that hold for manifolds (2), so, if K is a manifold, they remain true on subdivision. We shall see that no other expressions are ever invariant, but if K resembles a manifold in codimensions ⩽2r (in a sense defined below) that r of the relations continue to hold. 
Wall, C. T. C. Arithmetic Invariants of Subdivision of Complexes. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 92-96. doi: 10.4153/CJM-1966-012-9
@article{10_4153_CJM_1966_012_9,
     author = {Wall, C. T. C.},
     title = {Arithmetic {Invariants} of {Subdivision} of {Complexes}},
     journal = {Canadian journal of mathematics},
     pages = {92--96},
     year = {1966},
     volume = {18},
     number = {1},
     doi = {10.4153/CJM-1966-012-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-012-9/}
}
TY  - JOUR
AU  - Wall, C. T. C.
TI  - Arithmetic Invariants of Subdivision of Complexes
JO  - Canadian journal of mathematics
PY  - 1966
SP  - 92
EP  - 96
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-012-9/
DO  - 10.4153/CJM-1966-012-9
ID  - 10_4153_CJM_1966_012_9
ER  - 
%0 Journal Article
%A Wall, C. T. C.
%T Arithmetic Invariants of Subdivision of Complexes
%J Canadian journal of mathematics
%D 1966
%P 92-96
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-012-9/
%R 10.4153/CJM-1966-012-9
%F 10_4153_CJM_1966_012_9

[1] 1. Alexander, J. W., The combinatorial theory of complexes, Ann. of Math., 81 (1930), 292–320. Google Scholar

[2] 2. Klee, V., A combinatorial analogue of Poincaré's duality theorem, Can. J. Math., 16 (1964), 517–531. Google Scholar

[3] 3. Seifert, H. and Threlfall, W., Lehrbuch der Topologie (Leipzig, 1934). Google Scholar

Cité par Sources :