Homotopy idempotents on finitedimensional complexes split
Authors:
Harold M. Hastings and Alex Heller
Journal:
Proc. Amer. Math. Soc. 85 (1982), 619622
MSC:
Primary 55P99; Secondary 20E06, 20F05, 55P55
MathSciNet review:
660617
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Abstract 
References 
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Abstract: We prove that (unpointed) homotopy idempotents on finitedimensional complexes split, and describe some geometric consequences.
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P. Freyd and A. Heller, Splitting homotopy idempotents (to appear).
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geometric topology (Dubrovnik, 1981) Lecture Notes in Math.,
vol. 870, Springer, Berlin, 1981, pp. 23–36. MR 643520
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Alex
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of a conjecture of Borsuk, Ann. of Math. (2) 106
(1977), no. 1, 1–18. MR 0451247
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 [1]
 A. K. Bousfield and D. M. Kan, Homotopy limits, completions, and localizations, Lecture Notes in Math., vol. 304, SpringerVerlag, Berlin and New York, 1973. MR 0365573 (51:1825)
 [2]
 E. M. Brown, Cohomology theories, Ann. of Math. (2) 75 (1962), 467484. MR 0138104 (25:1551)
 [3]
 T. A. Chapman, On some applications of infinitedimensional manifolds to the theory of shape, Fund. Math. 76 (1972), 181193. MR 0320997 (47:9530)
 [4]
 T. A. Chapman and L. Siebenmann, Finding a boundary for a Hilbert cube manifold, Acta Math. 139 (1976), 171208. MR 0425973 (54:13922)
 [5]
 J. Dydak, A simple proof that pointed, connected FANRspaces are regular fundamental retracts of ANR's, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 5562. MR 0442918 (56:1293)
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 J. Dydak and H. M. Hastings, Homotopy idempotents on twodimensional complexes split, Proc. Internat. Conf. on Geometric Topology (Warsaw, 1978), (ed. K. Borsuk and A. Kirkor), PWN, Warsaw, 1980, pp. 127133. MR 656726 (83h:55013)
 [7]
 J. Dydak and J. Segal, Shape theory, Lecture Notes in Math., vol. 688, SpringerVerlag, Berlin and New York, 1978. MR 520227 (80h:54020)
 [8]
 D. A. Edwards and R. Geoghegan, Shapes of complexes, ends of manifolds, homotopy limits, and the Wall obstruction, Ann. of Math. (2) 101 (1975), 521535; Correction 104 (1976), 379. MR 0375330 (51:11525)
 [9]
 D. A. Edwards and H. M. Hastings, Čech and Steenrod homotopy theory, with applications to geometric topology, Lecture Notes in Math., vol. 542, SpringerVerlag, Berlin and New York, 1976. MR 0428322 (55:1347)
 [10]
 P. Freyd, Splitting homotopy idempotents, Proc. Conf. on Categorical Algebra (La Jolla 1965), (ed. S. Eilenberg and G. M. Kelley), Springer, Berlin and New York, 1966, pp. 173176. MR 0206069 (34:5894)
 [11]
 P. Freyd and A. Heller, Splitting homotopy idempotents (to appear).
 [12]
 H. M. Hastings and A. Heller, Splitting homotopy idempotents, Conf. on Shape and ProHomotopy (Dubrovnik, 1981), (ed. S. Mardešić and J. Segal), Lecture Notes in Math., vol. 870, SpringerVerlag, Berlin and New York, 1981, pp. 2336. MR 643520 (83a:55017)
 [13]
 A. Heller, On the representability of homotopy functors (to appear). MR 616562 (82h:55012)
 [14]
 P. J. Hilton and S. Wiley, Homology theory: an introduction to algebraic topology, Cambridge, 1962.
 [15]
 J. Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962), 337341. MR 0159327 (28:2544)
 [16]
 J. West, Mapping Hilbert cube manifolds to ANR's: A solution to a conjecture of Borsuk, Ann. of Math. (2) 106 (1977), 118. MR 0451247 (56:9534)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198206606175
PII:
S 00029939(1982)06606175
Article copyright:
© Copyright 1982 American Mathematical Society
