# Loop spaces of the Q-construction

Fundamenta Mathematicae (2000)

- Volume: 164, Issue: 1, page 71-95
- ISSN: 0016-2736

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topNeeman, A.. "Loop spaces of the Q-construction." Fundamenta Mathematicae 164.1 (2000): 71-95. <http://eudml.org/doc/212449>.

@article{Neeman2000,

abstract = {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.},

author = {Neeman, A.},

journal = {Fundamenta Mathematicae},

keywords = {-construction; -theory for triangulated categories; loop space},

language = {eng},

number = {1},

pages = {71-95},

title = {Loop spaces of the Q-construction},

url = {http://eudml.org/doc/212449},

volume = {164},

year = {2000},

}

TY - JOUR

AU - Neeman, A.

TI - Loop spaces of the Q-construction

JO - Fundamenta Mathematicae

PY - 2000

VL - 164

IS - 1

SP - 71

EP - 95

AB - 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.

LA - eng

KW - -construction; -theory for triangulated categories; loop space

UR - http://eudml.org/doc/212449

ER -

## References

top- [1] C. H. Giffen, Loop spaces for the Q-construction, J. Pure Appl. Algebra 52 (1988), 1-30. Zbl0655.18008
- [2] C. H. Giffen, Unitary algebraic Witt- and K-theories, preprint.
- [3] H. Gillet and D. R. Grayson, The loop space of the Q-construction, Illinois J. Math. 31 (1987), 574-597. Zbl0628.55011
- [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.
- [5] D. R. Grayson, Exterior power operations on higher K-theory, K-Theory 3 (1989), 247-260. Zbl0701.18007
- [6] J J. F. Jardine, The multiple Q-construction, Canad. J. Math. 39 (1987), 1174-1209. Zbl0656.55007
- [7] A. Neeman, K-theory for triangulated categories I(A), Asian J. Math. 1 (1997), 330-417. Zbl0906.19002
- [8] A. Neeman, K-theory for triangulated categories I(B), ibid. 1 (1997), 435-529. Zbl0906.19003
- [9] A. Neeman, K-theory for triangulated categories II, ibid. 2 (1998), 1-125. Zbl0923.19002
- [10] A. Neeman, K-theory for triangulated categories III(A), ibid. 2 (1998), 495-594. Zbl0937.19001
- [11] A. Neeman, K-theory for triangulated categories III(B), ibid. 3 (1999), 555-606.
- [12] D. Quillen, Higher algebraic K-theory I, in: Algebraic K-Theory I, Lecture Notes in Math. 341, Springer, 1973, 85-147. Zbl0292.18004
- [13] G. Segal, Categories and cohomology theories, Topology 13 (1974), 293-312. Zbl0284.55016

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