no. 4
A Poincaré duality type theorem for polyhedra
Annales de l'Institut Fourier, Tome 22 (1972) no. 4, pp. 47-58.

Si X est un polyèdre de dimension n, en employant des techniques géométriques, nous construisons des groupes H p (X) Δ et H p (X) Δ avec des isomorphismes naturels H p (X) Δ ≃H n-p (X) et H p (X) Δ ≃H n-p (X) induisant un accouplement d’intersection.

Ces groupes donnent une interprétation géométrique des deux suites spectrales étudiées par Zeeman et nous permettent de prouver une conjecture de Zeeman à leur sujet.

If X is a n-dim polyhedran, then using geometric techniques, we construct groups H p (X) Δ and H p (X) Δ such that there are natural isomorphisms H p (X) Δ ≃H n-p (X) and H p (X) Δ ≃H n-p (X) which induce an intersection pairing. These groups give a geometric interpretation of two spectral sequences studied by Zeeman and allow us to prove a conjecture of Zeeman about them.

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     author = {Gordon, Gerald Leonard},
     title = {A {Poincar\'e} duality type theorem for polyhedra},
     journal = {Annales de l'Institut Fourier},
     pages = {47--58},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {22},
     number = {4},
     year = {1972},
     doi = {10.5802/aif.434},
     zbl = {0234.55012},
     mrnumber = {49 #3904},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.434/}
}
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Gordon, Gerald Leonard. A Poincaré duality type theorem for polyhedra. Annales de l'Institut Fourier, Tome 22 (1972) no. 4, pp. 47-58. doi : 10.5802/aif.434. https://aif.centre-mersenne.org/articles/10.5802/aif.434/

[1] G. L. Gordon, The residue calculus in several complex variables. (To appear). | Zbl

[2] S. Lefschetz, Topology, Chelsea, New York, 1956. | Zbl

[3] R. G. Swan, The Theory of Sheaves, University of Chicago Press, Chicago, 1964. | Zbl

[4] E. C. Zeeman, Dihomology III, Proceedings of the London Math. Soc., (3), Vol. 13 (1963), pp. 155-183. | Zbl

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