Loop spaces of the Q-construction
Neeman, A.
Fundamenta Mathematicae, Tome 163 (2000), p. 71-95 / Harvested from The Polish Digital Mathematics Library
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Giffen in [1], and Gillet-Grayson in [3], independently found a simplicial model for the loop space on Quillen's Q-construction. Their proofs work for exact categories. Here we generalise the results to the K-theory of triangulated categories. The old proofs do not generalise. Our new proof, aside from giving the generalised result, can also be viewed as an amusing new proof of the old theorems of Giffen and Gillet-Grayson.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212449 
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Neeman, A. Loop spaces of the Q-construction. Fundamenta Mathematicae, Tome 163 (2000) pp. 71-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv164i1p71bwm/

[00000] [1] C. H. Giffen, Loop spaces for the Q-construction, J. Pure Appl. Algebra 52 (1988), 1-30. | Zbl 0655.18008

[00001] [2] C. H. Giffen, Unitary algebraic Witt- and K-theories, preprint.

[00002] [3] H. Gillet and D. R. Grayson, The loop space of the Q-construction, Illinois J. Math. 31 (1987), 574-597. | Zbl 0628.55011

[00003] [4] D. R. Grayson, Higher algebraic K-theory II (after D. Quillen), in: Algebraic K-Theory, Lecture Notes in Math. 551, Springer, 1976, 217-240.

[00004] [5] D. R. Grayson, Exterior power operations on higher K-theory, K-Theory 3 (1989), 247-260. | Zbl 0701.18007

[00005] [6] J J. F. Jardine, The multiple Q-construction, Canad. J. Math. 39 (1987), 1174-1209. | Zbl 0656.55007

[00006] [7] A. Neeman, K-theory for triangulated categories I(A), Asian J. Math. 1 (1997), 330-417. | Zbl 0906.19002

[00007] [8] A. Neeman, K-theory for triangulated categories I(B), ibid. 1 (1997), 435-529. | Zbl 0906.19003

[00008] [9] A. Neeman, K-theory for triangulated categories II, ibid. 2 (1998), 1-125. | Zbl 0923.19002

[00009] [10] A. Neeman, K-theory for triangulated categories III(A), ibid. 2 (1998), 495-594. | Zbl 0937.19001

[00010] [11] A. Neeman, K-theory for triangulated categories III(B), ibid. 3 (1999), 555-606.

[00011] [12] D. Quillen, Higher algebraic K-theory I, in: Algebraic K-Theory I, Lecture Notes in Math. 341, Springer, 1973, 85-147. | Zbl 0292.18004

[00012] [13] G. Segal, Categories and cohomology theories, Topology 13 (1974), 293-312. | Zbl 0284.55016