A simpler approximation to 𝑄𝑋

Caruso, Jeffrey L.

doi:10.1090/S0002-9947-1981-0607114-4

A simpler approximation to $QX$
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by Jeffrey L. Caruso PDF

Trans. Amer. Math. Soc. 265 (1981), 163-167 Request permission

Abstract:

McDuff’s construction ${C^ \pm }(M)$ of a space of positive and negative particles is modified to a space ${C^ \pm }({R^\infty },X)$, which is weakly homotopy equivalent to ${\Omega ^\infty }{\Sigma ^\infty }X$, for a locally equi-connected, nondegenerately based space $X$.

References

J. Caruso and S. Waner, An approximation to $\Omega ^{n}\Sigma ^{n}X$, Trans. Amer. Math. Soc. 265 (1981), no. 1, 147–162. MR 607113, DOI 10.1090/S0002-9947-1981-0607113-2
F. R. Cohen, J. P. May, and L. R. Taylor, Splitting of certain spaces $CX$, Math. Proc. Cambridge Philos. Soc. 84 (1978), no. 3, 465–496. MR 503007, DOI 10.1017/S0305004100055298
James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
Eldon Dyer and S. Eilenberg, An adjunction theorem for locally equiconnected spaces, Pacific J. Math. 41 (1972), 669–685. MR 319143

The homotopical foundations of algebraic topology

J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, Vol. 347, Springer-Verlag, Berlin-New York, 1973. MR 0420609
Dusa McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975), 91–107. MR 358766, DOI 10.1016/0040-9383(75)90038-5
Graeme Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973), 213–221. MR 331377, DOI 10.1007/BF01390197