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

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 Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR**0365573****[2]**W. G. Dwyer and D. M. Kan,*Homology and cohomology of \bfPi-algebras*, Trans. Amer. Math. Soc.**342**(1994), no. 1, 257–273. MR**1147399**, 10.1090/S0002-9947-1994-1147399-0**[3]**Daniel Quillen,*On the (co-) homology of commutative rings*, Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 65–87. MR**0257068****[4]**Christopher R. Stover,*A van Kampen spectral sequence for higher homotopy groups*, Topology**29**(1990), no. 1, 9–26. MR**1046622**, 10.1016/0040-9383(90)90022-C**[5]**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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DOI:
https://doi.org/10.1090/S0002-9939-1994-1169024-0

Article copyright:
© Copyright 1994
American Mathematical Society