Homotopy colimits - comparison lemmas for combinatorial applications

Journal fur die Reine und Angewandte Mathematik

Volumn 1999, Issue 509, 1999, Pages 117-149

  Welker, Volkmar ^a   Ziegler, Günter M ^a   Zivaljevic, Rade T ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039446402     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crll.1999.509.117     Document Type: Article

References (51)

1. M. Aschbacher and S. Smith, On Quillen#x0027;s conjecture for the -subgroups complex Ann. Math. (2) 137 (1993), 473-529.
2. E. Babson, A Combinatorial Flag Space PhD thesis, MIT, 1993.
3. C. Balteanu, Z. Fiedorowicz, R. Schwänzl, R. Vogt, Iterated monoidal categories II preprint 1998.
4. A. Björner, Topological methods In: R. Graham, M. Grötschel and L. Lovász, ed. Handbook of Combinatorics North-Holland, Amsterdam (1995), 1819-1872.
5. A. Björner, A generalized homotopy complementation formula Discr. Math. 193 (1998), 85-91.
6. A. Björner and J.W. Walker, A homotopy complementation formula for partially ordered sets Europ. J. Comb. 4 (1983), 11-19.
7. M. Bousfield and D. M. Kan, Homotopy Limits, Completions and Localizations Springer Lect. Notes Math. 304, Berlin-Heidelberg-New York 1972.
8. R. Brown, Elements of Modern Topology McGraw-Hill, London 1968.
9. V.I. Danilov, The geometry of toric varieties Russ. Math. Surv. 33 (2) (1978), 97-151.
10. A. Dold and R. Thom, Quasifaserungen und unendliche symmetrische Produkte Ann. Math. 67 (2) (1958), 239-281.
11. W. G. Dwyer and D.M. Kan, Function complexes for diagrams of simplicial sets Proc. Kon. Ned. Akad. van Wetensch. A86 (the same as) Ind. Math. 45 (1983), 139-147.
12. W. G. Dwyer and D. M. Kan, A classification theorem for diagrams of simplicial sets Topology 23 (2) (1984), 139-155.
13. G. Ewald, Combinatorial Convexity and Algebraic Geometry Springer Grad. Texts Math. 168, Berlin-Heidelberg-New York 1996.
14. E. Dror Farjoun, Homotopy and homology of diagrams of spaces in: Proc. Workshop #x201C;Algebraic Topology” (Seattle/Wash. 1985), Springer Lecture Notes Math. 1286, (1987), 93-124.
15. E. Dror Farjoun, Cellular Spaces, Null Spaces and Homotopy Localization Springer Lect. Notes Math. 1622, Berlin-Heidelberg-New York 1991.
16. E. Dror Farjoun and A. Zabrodsky, Homotopy equivalence between diagrams of spaces J. Pure Appl. Algebra 41 (1986), 169-182.
17. S. Fischli and D. Yavin, Which 4-manifolds are toric varieties? Math. Z. 215 (1994), 179-185.
18. W. Fulton, Introduction to Toric Varieties Ann. Math. Stud. 131, Princeton University Press, 1993.
19. P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory Springer Erg. Math. Grenzgeb. 35, Berlin-New York 1967.
20. M. Goresky and R. MacPherson, Stratified Morse Theory Springer Erg. Math. Grenzgeb. 14, Berlin-Heidelberg-New York 1988.
21. J. Hollender and R.M. Vogt, Modules of topological spaces applications to homotopy limits and Ex structures. Arch. Math. (Basel) 59 (1992), 115-129.
22. J.F. Kraus, Mayer-Vietoris-Prinzipien for Cofaserungen Math. Ann. 231 (1977), 47-53.
23. J. Lillig, A union theorem for cofibrations Arch. Math. (Basel) 24 (1973), 410-415.
24. A.T. Lundell and S. Weingram, The Topology of CW Complexes Van Nostrand Reinhold, New York 1966
25. J.P. May, Simplicial Objects in Algebraic Topology Van Nostrand Math. Stud. 11, Princeton NJ 1967.
26. J. P. May, The Geometry of Iterated Loop Spaces Springer Lect. Notes Math. 271, Berlin-Heidelberg-New York 1972.
27. J.P. May, Spaces group completions and permutative categories, in: New Developments in Topology (G. Segal, ed.), London Math. Soc. Lect. Note Ser. 11 (1974), 61-93.
28. M. McConnell, Rational homology of toric varieties Proc. Amer. Math. Soc. 105 (4) (1989), 986-991.
29. J. Milnor, The geometric realization of a semi-simplicial complex Ann. Math. (2) 65 (1957), 357-362.
30. J. Milnor, On spaces having the homotopy type of a CW-complex Trans. Amer. Math. Soc. 90 (1959), 272-280.
31. J. Pulkus and V. Welker, On the homotopy type of the /7-subgroup complex for finite solvable groups preprint 1995.
32. D. Puppe, Homotopiemengen und induzierte Abbildungen I, Math. Z. 69 (1958), 299-344.
33. D. Quillen, Higher Algebraic A-Theory: I Springer Lect. Notes Math. 341, Berlin-Heidelberg-New York 1973.
34. D. Quillen, Homotopy properties of the poset of nontrivial p-subgroups of a group Adv. Math. 28 (1978), 101-128.
35. K.S. Sarkaria, A generalized Kneser conjecture J. Comb. Th. (B) 49 (1990), 236-240.
36. C. Schaper, Suspensions of affine arrangements Math. Ann. 309 (1997), 463-473.
37. G.B. Segal, Classifying spaces and spectral sequences Publ. Math. I.H.E.S. 34 (1968), 105-112.
38. G.B. Segal, Categories and cohomology theories Publ. Math. I.H.E.S. 13 (1974), 293-312.
39. R.P. Stanley, Enumerative Combinatorics, I, Wadsworth and Brooks/Cole Monterey, CA, 1986.
40. B. Sturmfels and G. M. Ziegler, Extension spaces of oriented matroids Disc. Comp. Geom. 10 (1993), 23-45.
41. S. Sundaram and V. Welker, Group actions on arrangements of linear subspaces and applications to configuration spaces Trans. Amer. Math. Soc. 239 (1997), 1389-1420.
42. T. tom Dieck, Partitions of unity in homotopy theory Comp. Math. 23 (1973), 159-161.
43. V.A. Vassiliev, Complements of Discriminants of Smooth Maps: Topology and Applications Transl. Math. Monogr. 98, Amer. Math. Soc. Providence, RI, revised edition 1994.
44. R.M. Vogt, Homotopy limits and colimits Math. Z. 134 (1973), 11-52.
45. J. W. Walker, Homotopy type and Euler characteristic of partially ordered sets Europ. J. Combin. 2 (1981), 373-384.
46. J. W. Walker, Canonical homeomorphisms of posets Europ. J. Combin. 9 (1988), 97-107.
47. G. W. Whitehead, Elements of Homotopy Theory Springer Grad. Texts Math. 61, Berlin-Heidelberg-New York 1978.
48. D. Yavin, The Intersection Homology with Twisted Coefficients of Toric Varieties PhD thesis, MIT, 1990.
49. G.M. Ziegler and R. T. Živaljeviç, Homotopy types of subspace arrangements via diagrams of spaces Math. Ann. 295 (1993), 527-548.
50. R.T. Živaljeviç, Topological methods in: CRC Handbook on Discrete and Computational Geometry (J. E. Goodman, J. O#x0027;Rourke, eds.), CRC Press, Boca Raton (1997), 209-224.
51. R.T. Živaljeviç, Combinatorics of topological posets: Homotopy complementation formulas Adv. Appl. Math. 21 (1998), 547-574.