Poset fiber theorems

Björner, Anders; Wachs, Michelle; Welker, Volkmar

doi:10.1090/S0002-9947-04-03496-8

Poset fiber theorems
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by Anders Björner, Michelle L. Wachs and Volkmar Welker

Trans. Amer. Math. Soc. 357 (2005), 1877-1899

DOI: https://doi.org/10.1090/S0002-9947-04-03496-8

Published electronically: July 22, 2004

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Abstract:

Suppose that $f:P \to Q$ is a poset map whose fibers $f^{-1}(Q_{\le q})$ are sufficiently well connected. Our main result is a formula expressing the homotopy type of $P$ in terms of $Q$ and the fibers. Several fiber theorems from the literature (due to Babson, Baclawski and Quillen) are obtained as consequences or special cases. Homology, Cohen-Macaulay, and equivariant versions are given, and some applications are discussed.

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