On the suspension homomorphism

S. Dragotti; G. Magro; L. Parlato

Bollettino dell'Unione Matematica Italiana (2002)

  • Volume: 5-B, Issue: 1, page 247-257
  • ISSN: 0392-4041

Abstract

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In this paper we investigate the conditions for the suspension homomorphism s : Θ r - 1 F ⁢ S n - 1 , x 0 → Θ r F ⁢ S n , x 0 is onto or an isomorphism.

How to cite

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Dragotti, S., Magro, G., and Parlato, L.. "On the suspension homomorphism." Bollettino dell'Unione Matematica Italiana 5-B.1 (2002): 247-257. <http://eudml.org/doc/195222>.

@article{Dragotti2002,
abstract = {In this paper we investigate the conditions for the suspension homomorphism $$s \colon \Theta^\{\mathcal\{F\}\}\_\{r-1\}(S^\{n-1\}, x\_\{0\}) \to \Theta ^\{\mathcal\{F\}\}\_\{r\}(S^\{n\}, x\_\{0\})$$ is onto or an isomorphism. },
author = {Dragotti, S., Magro, G., Parlato, L.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {247-257},
publisher = {Unione Matematica Italiana},
title = {On the suspension homomorphism},
url = {http://eudml.org/doc/195222},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Dragotti, S.
AU - Magro, G.
AU - Parlato, L.
TI - On the suspension homomorphism
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/2//
PB - Unione Matematica Italiana
VL - 5-B
IS - 1
SP - 247
EP - 257
AB - In this paper we investigate the conditions for the suspension homomorphism $$s \colon \Theta^{\mathcal{F}}_{r-1}(S^{n-1}, x_{0}) \to \Theta ^{\mathcal{F}}_{r}(S^{n}, x_{0})$$ is onto or an isomorphism.
LA - eng
UR - http://eudml.org/doc/195222
ER -

References

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  3. DRAGOTTI, S.- ESPOSITO, R.- MAGRO, G., Construction of functors connecting homology and homotopy theories, Proc. of Amer. Math. Soc., 120 (1994), 635-646. Zbl0814.55001MR1165052
  4. DRAGOTTI, S.- ESPOSITO, R.- MAGRO, G.- PARLATO, L., Geometric representation of homology functor, Ricerche di Matematica, 45 (1996), 3-12. Zbl0936.55003MR1469718
  5. DRAGOTTI, S.- MAGRO, G., A representation of homotopy theory by homotopy spheres, Ricerche di Matematica, 46 (1997), 13-22. Zbl0949.55005MR1615723
  6. DRAGOTTI, S.- MAGRO, G.- PARLATO, L., On the groups Θ n F of a sphere, Boll. U.M.I. (8) 3-B (2000), 337-346. Zbl0962.55007MR1769990
  7. ESPOSITO, R.- PARLATO, L., I teoremi di Hurewicz e Whitehead per funtori omotopici associati a manifold classes, Ricerche di Matematica, 44, (1995), 359-368. Zbl0916.55008MR1469707
  8. FREUDENTHAL, H., Compositio Math, 5 (1937), 299-314. JFM63.1161.02
  9. MAUNDER, C. R. F., Algebraic topology, Van Nostrand, London, 1970. Zbl0205.27302
  10. ROURKE, C. P.- SANDERSON, B. J., Introduction to PL topology, Ergeb. Mat. Band. 69, Springer-Verlag, Berlin and New York, 1972. Zbl0254.57010MR350744
  11. BUONCRISTIANO, S.- ROURKE, C. P.- SANDERSON, B. J., A geometric approach in homology theory, Cambridge University Press - London - New York, 1976. Zbl0315.55002MR413113
  12. SPANIER, E. H., Algebraic Topology, McGraw-Hill, New York, 1966. Zbl0145.43303MR210112
  13. WHITEHEAD, J. H. C., Note on suspension, Quart. J. Math. Oxford (2), 1 (1950), 9-22. Zbl0035.24802MR34579

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