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Cellular strings on polytopes

Authors: L. J. Billera, M. M. Kapranov and B. Sturmfels
Journal: Proc. Amer. Math. Soc. 122 (1994), 549-555
MSC: Primary 52B40; Secondary 52B99, 55P99, 57T30
MathSciNet review: 1205482
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Abstract: The complex of cellular strings with respect to a generic linear functional on a d-dimensional convex polytope has the homotopy type of the $ (d - 2)$-sphere. This result was conjectured in a special case by H.-J. Baues.

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  • [1] J. F. Adams, On the cobar construction, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 409-412. MR 0079266 (18:59c)
  • [2] H. J. Baues, Geometry of loop spaces and the cobar construction, Mem. Amer. Math. Soc., vol. 25, Amer. Math. Soc., Providence, RI, 1980. MR 567799 (81m:55010)
  • [3] L. J. Billera and B. Sturmfels, Fiber polytopes, Ann. of Math. (2) 135 (1992), 527-549. MR 1166643 (93e:52019)
  • [4] L. J. Billera, P. Filliman, and B. Sturmfels, Constructions and complexity of secondary polytopes, Adv. Math. 83 (1990), 155-179. MR 1074022 (92d:52028)
  • [5] A. Björner, Essential chains and homotopy type of posets, Proc. Amer. Math. Soc. 116 (1992), 1179-1181. MR 1140664 (94b:06001)
  • [6] P. Gabriel and M. Zisman, Calculus of functions and homotopy theory, Ergebnisse der Math., bd. 35, Springer, Berlin, 1967.
  • [7] I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Newton polytopes of the classical discriminant and resultant, Adv. Math. 84 (1990), 237-254. MR 1080979 (92a:14060)
  • [8] R. J. Milgram, Iterated loop spaces, Ann. of Math. (2) 84 (1966), 386-403. MR 0206951 (34:6767)
  • [9] D. Quillen, Higher algebraic K-theory: I, Higher K-Theories (H. Bass, ed.), Lecture Notes in Math., vol. 341, Springer, New York, 1973, pp. 77-139. MR 0338129 (49:2895)
  • [10] R. Rado, An inequality, J. London Math. Soc. (2) 27 (1952), 1-6. MR 0045168 (13:539e)
  • [11] B. Sturmfels and G. Ziegler, Extension spaces of oriented matroids, Discrete Comput. Geom. 10 (1993), 23-45. MR 1215321 (94i:52015)

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Article copyright: © Copyright 1994 American Mathematical Society

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