Poset Fiber Theorems

Anders Bj\"orner, Michelle L. Wachs and Volkmar Welker

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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