A -algebra spectral sequence for function spaces

Authors:
W. G. Dwyer, D. M. Kan, J. H. Smith and C. R. Stover

Journal:
Proc. Amer. Math. Soc. **120** (1994), 615-621

MSC:
Primary 55P15; Secondary 55T99

DOI:
https://doi.org/10.1090/S0002-9939-1994-1169024-0

MathSciNet review:
1169024

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Abstract: We construct a new kind of spectral sequence which is in some ways analogous to the unstable Adams spectral sequence. This new spectral sequence converts primary information about the homotopy groups of two spaces and into information about the homotopy groups of the function space of maps from to .

**[1]**A. K. Bousfield and D. M. Kan,*Homotopy limits, completions and localizations*, Lecture Notes in Math., vol. 304, Springer, Berlin, 1972. MR**0365573 (51:1825)****[2]**W. G. Dwyer and D. M. Kan,*Homology and cohomology of*-*algebras*, Trans. Amer. Math. Soc. (to appear). MR**1147399 (94h:55027)****[3]**D. G. Quillen,*On the*(*co*)-*homology of commutative rings*, Categorical Algebra, Proc. Sympos. Pure Math., vol. 17, Amer. Math. Soc., Providence, RI, 1970, pp. 65-87. MR**0257068 (41:1722)****[4]**C. R. Stover,*A van Kampen spectral sequence for higher homotopy groups*, Topology**29**(1990), 9-26. MR**1046622 (91h:55011)****[5]**G. W. Whitehead,*Elements of homotopy theory*, Graduate Texts in Math., vol. 61, Springer, Berlin, 1978. MR**516508 (80b:55001)**

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1169024-0

Article copyright:
© Copyright 1994
American Mathematical Society