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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Smooth extensions for finite CW complexes
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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
  • —, Relative K-homology and ${C^\ast }$-algebra, manuscript.
  • 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, 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.
  • 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
  • —, The relation between Ext group and index of Fredholm n-tuples, preprint.
  • 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, Note on corbordism theory, Math. Notes, Princeton Univ. Press, Princeton, N.J., 1968.
  • George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, Springer-Verlag, New York-Berlin, 1978. MR 516508
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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