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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Poset fiber theorems


Authors: Anders Björner, Michelle L. Wachs and Volkmar Welker
Journal: Trans. Amer. Math. Soc. 357 (2005), 1877-1899
MSC (2000): Primary 05E25, 06A11, 55P10
Published electronically: July 22, 2004
MathSciNet review: 2115080
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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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Additional Information

Anders Björner
Affiliation: Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Email: bjorner@math.kth.se

Michelle L. Wachs
Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33124
Email: wachs@math.miami.edu

Volkmar Welker
Affiliation: Fachbereich Mathematik und Informatik, Universität Marburg, D-350 32 Marburg, Germany
Email: welker@mathematik.uni-marburg.de

DOI: https://doi.org/10.1090/S0002-9947-04-03496-8
Received by editor(s): July 25, 2002
Received by editor(s) in revised form: August 20, 2003
Published electronically: July 22, 2004
Additional Notes: The first author was supported by Göran Gustafsson Foundation for Research in Natural Sciences and Medicine, and by EC’s IHRP programme, grant HPRN-CT-2001-00272.
The second author was supported in part by National Science Foundation grants DMS 9701407 and DMS 0073760.
The third author was supported by Deutsche Forschungsgemeinschaft (DFG), and by EC’s IHRP programme, grant HPRN-CT-2001-00272.
Article copyright: © Copyright 2004 American Mathematical Society