Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Construction of functors connecting homology and homotopy theories

Authors: S. Dragotti, R. Esposito and G. Magro
Journal: Proc. Amer. Math. Soc. 120 (1994), 635-646
MSC: Primary 57Q20; Secondary 55N35, 55P65, 57P99
MathSciNet review: 1165052
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For each manifold class $ \mathcal{F}$ it is given a functor $ {\Theta ^\mathcal{F}}$ satisfying the Eilenberg and Steenrod axioms except the excision axiom. It provides a nice unification of geometric treatments of homology and homotopy theories.

References [Enhancements On Off] (What's this?)

  • [1] G. A. Anderson, Resolution of generalized polyhedral manifolds, Tôhoku Math. J. (2) 31 (1979), 495-517. MR 558680 (82g:57007)
  • [2] S. Buoncristiano, C. P. Rourke, and B. J. Sanderson, A geometric approach to homology theory, Cambridge Univ. Press, London and New York, 1976. MR 0413113 (54:1234)
  • [3] M. M. Cohen, Simplicial structures and transverse cellularity, Ann. of Math. (2) 85 (1967), 218-245. MR 0210143 (35:1037)
  • [4] S. Dragotti, R. Esposito, and G. Magro, $ \mathcal{F}$-varietà e funzioni dual cellulari, Ricerche Mat. 39 (1990), 21-33. MR 1101302 (92h:57035)
  • [5] S. T. Hu, Homotopy theory, Academic Press, New York and London, 1959. MR 0106454 (21:5186)
  • [6] C. P. Rourke and B. J. Sanderson, Introduction to $ PL$ topology, Ergeb. Math. Grenzgeb. (3), bd. 69, Springer-Verlag, Berlin and New York, 1972. MR 0350744 (50:3236)
  • [7] -, A geometric approach in homology theory, notes, Warwick Univ., Coventry, 1971.
  • [8] H. Seifert and W. Threlfall, Lehrbuch der topologie, Teubner Verlagsgesellschaft, Leipzig, 1934.
  • [9] E. H. Spanier, Algebraic topology, McGraw-Hill, New York, 1966. MR 0210112 (35:1007)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57Q20, 55N35, 55P65, 57P99

Retrieve articles in all journals with MSC: 57Q20, 55N35, 55P65, 57P99

Additional Information

Keywords: Manifold class, cobordism, homotopy functor
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society