# A Poincaré duality type theorem for polyhedra

Annales de l'institut Fourier (1972)

- Volume: 22, Issue: 4, page 47-58
- ISSN: 0373-0956

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topGordon, Gerald Leonard. "A Poincaré duality type theorem for polyhedra." Annales de l'institut Fourier 22.4 (1972): 47-58. <http://eudml.org/doc/74103>.

@article{Gordon1972,

abstract = {If $X$ is a $n$-dim polyhedran, then using geometric techniques, we construct groups $H_p(X)_\Delta $ and $H^p(X)_\Delta $ such that there are natural isomorphisms $H^p(X)_\Delta \simeq H_\{n-p\}(X)$ and $H_p(X)_\Delta \simeq H^\{n-p\}(X)$ 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.},

author = {Gordon, Gerald Leonard},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {4},

pages = {47-58},

publisher = {Association des Annales de l'Institut Fourier},

title = {A Poincaré duality type theorem for polyhedra},

url = {http://eudml.org/doc/74103},

volume = {22},

year = {1972},

}

TY - JOUR

AU - Gordon, Gerald Leonard

TI - A Poincaré duality type theorem for polyhedra

JO - Annales de l'institut Fourier

PY - 1972

PB - Association des Annales de l'Institut Fourier

VL - 22

IS - 4

SP - 47

EP - 58

AB - If $X$ is a $n$-dim polyhedran, then using geometric techniques, we construct groups $H_p(X)_\Delta $ and $H^p(X)_\Delta $ such that there are natural isomorphisms $H^p(X)_\Delta \simeq H_{n-p}(X)$ and $H_p(X)_\Delta \simeq H^{n-p}(X)$ 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.

LA - eng

UR - http://eudml.org/doc/74103

ER -

## References

top- [1] G. L. GORDON, The residue calculus in several complex variables. (To appear). Zbl0349.32002
- [2] S. LEFSCHETZ, Topology, Chelsea, New York, 1956. Zbl0045.25902
- [3] R. G. SWAN, The Theory of Sheaves, University of Chicago Press, Chicago, 1964. Zbl0119.25801
- [4] E. C. ZEEMAN, Dihomology III, Proceedings of the London Math. Soc., (3), Vol. 13 (1963), pp. 155-183. Zbl0109.41302

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