Homotopy Type of Intervals of the Second Higher Bruhat Orders
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268.38 KB
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Author(s)
McConville, Thomas
Date Issued
December 2017
Journal
Order
Publisher
Springer Netherlands
Citation
McConville, Thomas. “Homotopy Type of Intervals of the Second Higher Bruhat Orders.” Order 35, no. 3 (December 19, 2017): 515–524.
Version
Author's final manuscript
Abstract
The higher Bruhat order is a poset generalizing the weak order on permutations. Another special case of this poset is an ordering on simple wiring diagrams. For this case, we prove that every interval is either contractible or homotopy equivalent to a sphere. This partially proves a conjecture due to Reiner. Our proof uses some tools developed by Felsner and Weil to study wiring diagrams. Keywords: Higher Bruhat, Order complex, Mobius function, Wiring diagram, Rhombic tiling
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s11083-017-9446-z
