Homotopy Type of Intervals of the Second Higher Bruhat Orders
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 t...
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| Format: | Article |
| Language: | English |
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Springer Netherlands
2018
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| Online Access: | http://hdl.handle.net/1721.1/119674 https://orcid.org/0000-0001-9276-4291 |
| _version_ | 1811097713868013568 |
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| author | McConville, Thomas |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics McConville, Thomas |
| author_sort | McConville, Thomas |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T17:03:44Z |
| format | Article |
| id | mit-1721.1/119674 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:03:44Z |
| publishDate | 2018 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/1196742022-10-03T10:07:51Z Homotopy Type of Intervals of the Second Higher Bruhat Orders McConville, Thomas Massachusetts Institute of Technology. Department of Mathematics McConville, Thomas 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 2018-12-18T15:05:19Z 2018-12-18T15:05:19Z 2017-12 2018-10-05T03:42:23Z Article http://purl.org/eprint/type/JournalArticle 0167-8094 1572-9273 http://hdl.handle.net/1721.1/119674 McConville, Thomas. “Homotopy Type of Intervals of the Second Higher Bruhat Orders.” Order 35, no. 3 (December 19, 2017): 515–524. https://orcid.org/0000-0001-9276-4291 en https://doi.org/10.1007/s11083-017-9446-z Order 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. Springer Science+Business Media B.V., part of Springer Nature application/pdf Springer Netherlands Springer Netherlands |
| spellingShingle | McConville, Thomas Homotopy Type of Intervals of the Second Higher Bruhat Orders |
| title | Homotopy Type of Intervals of the Second Higher Bruhat Orders |
| title_full | Homotopy Type of Intervals of the Second Higher Bruhat Orders |
| title_fullStr | Homotopy Type of Intervals of the Second Higher Bruhat Orders |
| title_full_unstemmed | Homotopy Type of Intervals of the Second Higher Bruhat Orders |
| title_short | Homotopy Type of Intervals of the Second Higher Bruhat Orders |
| title_sort | homotopy type of intervals of the second higher bruhat orders |
| url | http://hdl.handle.net/1721.1/119674 https://orcid.org/0000-0001-9276-4291 |
| work_keys_str_mv | AT mcconvillethomas homotopytypeofintervalsofthesecondhigherbruhatorders |