A stably contractible algebra which is not contractible
Author:
Marius Dadarlat
Journal:
Proc. Amer. Math. Soc. 142 (2014), 32173220
MSC (2010):
Primary 46L35, 46L80, 19K35
Published electronically:
June 5, 2014
MathSciNet review:
3223377
Fulltext PDF
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Abstract: We exhibit a separable commutative algebra such that is homotopy equivalent to zero, without being so for any .
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 [1]
 Marius Dadarlat and James McClure, When are two commutative algebras stably homotopy equivalent?, Math. Z. 235 (2000), no. 3, 499523. MR 1800209 (2001k:46080), http://dx.doi.org/10.1007/s002090000143
 [2]
 M. Dădărlat and A. Némethi, Shape theory and (connective) theory, J. Operator Theory 23 (1990), no. 2, 207291. MR 1066807 (91j:46092)
 [3]
 Allen Hatcher, Algebraic topology, Cambridge University Press, Cambridge, 2002. MR 1867354 (2002k:55001)
 [4]
 Jonathan Rosenberg, The role of theory in noncommutative algebraic topology, Operator algebras and theory (San Francisco, Calif., 1981) Contemp. Math., vol. 10, Amer. Math. Soc., Providence, R.I., 1982, pp. 155182. MR 658514 (84h:46097)
 [5]
 Graeme Segal, homology theory and algebraic theory, theory and operator algebras (Proc. Conf., Univ. Georgia, Athens, Ga., 1975), Lecture Notes in Math., Vol. 575, Springer, Berlin, 1977, pp. 113127. MR 0515311 (58 #24242)
 [6]
 H. Thiel,
Inductive limits of projective algebras, preprint, May 2011, arXiv:1105.1979.
 [7]
 Klaus Thomsen, Homotopy classes of homomorphisms between stable algebras and their multiplier algebras, Duke Math. J. 61 (1990), no. 1, 67104. MR 1068380 (91m:46115), http://dx.doi.org/10.1215/S0012709490061046
 [8]
 George W. Whitehead, Elements of homotopy theory, Graduate Texts in Mathematics, vol. 61, SpringerVerlag, New York, 1978. MR 516508 (80b:55001)
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Additional Information
Marius Dadarlat
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
mdd@math.purdue.edu
DOI:
http://dx.doi.org/10.1090/S000299392014121137
Received by editor(s):
February 28, 2012
Received by editor(s) in revised form:
October 15, 2012
Published electronically:
June 5, 2014
Additional Notes:
The author was partially supported by NSF grants #DMS–0801173 and #DMS–1101305
Communicated by:
Marius Junge
Article copyright:
© Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
