Poset fiber theorems

Anders Björner, Michelle L Galloway, Volkmar Welker

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

Suppose that f : P → Q is a poset map whose fibers f -1(Q ≤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.

Original languageEnglish (US)
Pages (from-to)1877-1899
Number of pages23
JournalTransactions of the American Mathematical Society
Volume357
Issue number5
DOIs
StatePublished - May 2005

Fingerprint

Poset
Fiber
Fibers
Theorem
Homotopy Type
Cohen-Macaulay
Equivariant
Homology

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Poset fiber theorems. / Björner, Anders; Galloway, Michelle L; Welker, Volkmar.

In: Transactions of the American Mathematical Society, Vol. 357, No. 5, 05.2005, p. 1877-1899.

Research output: Contribution to journalArticle

Björner, Anders ; Galloway, Michelle L ; Welker, Volkmar. / Poset fiber theorems. In: Transactions of the American Mathematical Society. 2005 ; Vol. 357, No. 5. pp. 1877-1899.
@article{9b61609f92e84e19aa13228aa4ce8649,
title = "Poset fiber theorems",
abstract = "Suppose that f : P → Q is a poset map whose fibers f -1(Q ≤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.",
author = "Anders Bj{\"o}rner and Galloway, {Michelle L} and Volkmar Welker",
year = "2005",
month = "5",
doi = "10.1090/S0002-9947-04-03496-8",
language = "English (US)",
volume = "357",
pages = "1877--1899",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "5",

}

TY - JOUR

T1 - Poset fiber theorems

AU - Björner, Anders

AU - Galloway, Michelle L

AU - Welker, Volkmar

PY - 2005/5

Y1 - 2005/5

N2 - Suppose that f : P → Q is a poset map whose fibers f -1(Q ≤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.

AB - Suppose that f : P → Q is a poset map whose fibers f -1(Q ≤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.

UR - http://www.scopus.com/inward/record.url?scp=18144413921&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18144413921&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-04-03496-8

DO - 10.1090/S0002-9947-04-03496-8

M3 - Article

AN - SCOPUS:18144413921

VL - 357

SP - 1877

EP - 1899

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 5

ER -