## Smooth extensions for finite CW complexes

HTML articles powered by AMS MathViewer

- by Guihua Gong PDF
- Trans. Amer. Math. Soc.
**342**(1994), 343-358 Request permission

## Abstract:

In this paper, we have completely classified the ${C_n}$-smooth elements of $\operatorname {Ext} (X)$ modulo torsion for*X*being an arbitrary finite CW complex.

## References

- M. F. Atiyah,
*Global theory of elliptic operators*, Proc. Internat. Conf. on Functional Analysis and Related Topics (Tokyo, 1969) Univ. Tokyo Press, Tokyo, 1970, pp. 21–30. MR**0266247** - Paul Baum and Ronald G. Douglas,
*Toeplitz operators and Poincaré duality*, Toeplitz centennial (Tel Aviv, 1981) Operator Theory: Advances and Applications, vol. 4, Birkhäuser, Basel-Boston, Mass., 1982, pp. 137–166. MR**669904**
—, - Bruce Blackadar,
*$K$-theory for operator algebras*, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986. MR**859867**, DOI 10.1007/978-1-4613-9572-0 - Raoul Bott and Loring W. Tu,
*Differential forms in algebraic topology*, Graduate Texts in Mathematics, vol. 82, Springer-Verlag, New York-Berlin, 1982. MR**658304** - L. G. Brown, R. G. Douglas, and P. A. Fillmore,
*Extensions of $C^*$-algebras and $K$-homology*, Ann. of Math. (2)**105**(1977), no. 2, 265–324. MR**458196**, DOI 10.2307/1970999 - Chieh Chen,
*A note on the classification of mappings of a $(2n-2)$-dimensional complex into an $n$ sphere*, Ann. of Math. (2)**51**(1950), 238–240. MR**33005**, DOI 10.2307/1969507
A. Connes, - Ronald G. Douglas,
*$C^{\ast }$-algebra extensions and $K$-homology*, Annals of Mathematics Studies, No. 95, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR**571362** - R. G. Douglas,
*On the smoothness of elements of Ext*, Topics in modern operator theory (Timişoara/Herculane, 1980), Operator Theory: Advances and Applications, vol. 2, Birkhäuser, Basel-Boston, Mass., 1981, pp. 63–69. MR**672816** - R. G. Douglas and Dan Voiculescu,
*On the smoothness of sphere extensions*, J. Operator Theory**6**(1981), no. 1, 103–111. MR**637004** - Guihua Gong,
*Smooth extensions for a finite CW complex*, Bull. Amer. Math. Soc. (N.S.)**22**(1990), no. 1, 73–77. MR**1003863**, DOI 10.1090/S0273-0979-1990-15844-6
—, - Brayton Gray,
*Homotopy theory*, Pure and Applied Mathematics, Vol. 64, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. An introduction to algebraic topology. MR**0402714** - Phillip A. Griffiths and John W. Morgan,
*Rational homotopy theory and differential forms*, Progress in Mathematics, vol. 16, Birkhäuser, Boston, Mass., 1981. MR**641551** - J. William Helton and Roger E. Howe,
*Integral operators: commutators, traces, index and homology*, Proceedings of a Conference Operator Theory (Dalhousie Univ., Halifax, N.S., 1973) Lecture Notes in Math., Vol. 345, Springer, Berlin, 1973, pp. 141–209. MR**0390829** - J. William Helton and Roger E. Howe,
*Traces of commutators of integral operators*, Acta Math.**135**(1975), no. 3-4, 271–305. MR**438188**, DOI 10.1007/BF02392022 - Sze-tsen Hu,
*Extension and classification of the mappings of a finite complex into a topological group of an $n$-sphere*, Ann. of Math. (2)**50**(1949), 158–173. MR**28029**, DOI 10.2307/1969359 - G. G. Kasparov,
*The operator $K$-functor and extensions of $C^{\ast }$-algebras*, Izv. Akad. Nauk SSSR Ser. Mat.**44**(1980), no. 3, 571–636, 719 (Russian). MR**582160**
R. Stong, - George W. Whitehead,
*Elements of homotopy theory*, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR**516508**

*Relative K-homology and*${C^\ast }$-

*algebra*, manuscript.

*Non commutative differential geometry*, Chapitres 1, 2, Publ. Math. Inst. Hautes Études Sci.

**62**(1986), 257-360. —,

*Cyclic cohomology and the tranverse fundamental class of a foliation*, Preprint, IHES M18417, 1984.

*The relation between Ext group and index of Fredholm n-tuples*, preprint.

*Note on corbordism theory*, Math. Notes, Princeton Univ. Press, Princeton, N.J., 1968.

## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**342**(1994), 343-358 - MSC: Primary 46L87; Secondary 19K33, 46M20
- DOI: https://doi.org/10.1090/S0002-9947-1994-1150013-1
- MathSciNet review: 1150013