Construction of functors connecting homology and homotopy theories
HTML articles powered by AMS MathViewer
- by S. Dragotti, R. Esposito and G. Magro PDF
- Proc. Amer. Math. Soc. 120 (1994), 635-646 Request permission
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
- Gerald A. Anderson, Resolutions of generalized polyhedral manifolds, Tohoku Math. J. (2) 31 (1979), no. 4, 495–517. MR 558680, DOI 10.2748/tmj/1178229733
- S. Buoncristiano, C. P. Rourke, and B. J. Sanderson, A geometric approach to homology theory, London Mathematical Society Lecture Note Series, No. 18, Cambridge University Press, Cambridge-New York-Melbourne, 1976. MR 0413113
- Marshall M. Cohen, Simplicial structures and transverse cellularity, Ann. of Math. (2) 85 (1967), 218–245. MR 210143, DOI 10.2307/1970440
- Sara Dragotti, Rosa Esposito, and Gaetano Magro, ${\scr F}$-manifolds and dual cellular functions, Ricerche Mat. 39 (1990), no. 1, 21–33 (Italian, with English summary). MR 1101302
- Sze-tsen Hu, Homotopy theory, Pure and Applied Mathematics, Vol. VIII, Academic Press, New York-London, 1959. MR 0106454
- C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972. MR 0350744 —, A geometric approach in homology theory, notes, Warwick Univ., Coventry, 1971. H. Seifert and W. Threlfall, Lehrbuch der topologie, Teubner Verlagsgesellschaft, Leipzig, 1934.
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 635-646
- MSC: Primary 57Q20; Secondary 55N35, 55P65, 57P99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1165052-X
- MathSciNet review: 1165052