Geodesic
On $f$-vectors and relative homology
Journal of Algebraic Combinatorics, Tome 9 (1999) no. 3, pp. 215-232.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We find strong necessary conditions on the $f$-vectors, Betti sequences, and relative Betti sequence of a pair of simplicial complexes. We also present an example showing that these conditions are not sufficient. If only the difference between two Betti sequences is specified, and not the individual Betti sequences, then the characterization is complete, and the characterization of all pairs of simplicial complexes matches the characterization of pairs of near-cones. Our necessary conditions rely upon a combinatorial decomposition of pairs of simplicial complexes that reflects the homology and relative homology of the complexes.
Keywords: $f$-vector, Betti sequence, relative homology, simplicial complex, decomposition 
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     author = {Duval, Art M.},
     title = {On $f$-vectors and relative homology},
     journal = {Journal of Algebraic Combinatorics},
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Duval, Art M. On $f$-vectors and relative homology. Journal of Algebraic Combinatorics, Tome 9 (1999) no. 3, pp. 215-232. http://geodesic.mathdoc.fr/item/JAC_1999__9_3_a5/