A Poincaré duality type theorem for polyhedra

Gerald Leonard Gordon

Annales de l'institut Fourier (1972)

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

Abstract

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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.

How to cite

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Gordon, 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

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  1. [1] G. L. GORDON, The residue calculus in several complex variables. (To appear). Zbl0349.32002
  2. [2] S. LEFSCHETZ, Topology, Chelsea, New York, 1956. Zbl0045.25902
  3. [3] R. G. SWAN, The Theory of Sheaves, University of Chicago Press, Chicago, 1964. Zbl0119.25801
  4. [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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