Branched Polymers and Hyperplane Arrangements
Original manuscript December 17, 2009
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer-Verlag
2013
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| Online Access: | http://hdl.handle.net/1721.1/80707 https://orcid.org/0000-0002-3964-8870 |
| _version_ | 1826200596959461376 |
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| author | Postnikov, Alexander Meszaros, Karola |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Postnikov, Alexander Meszaros, Karola |
| author_sort | Postnikov, Alexander |
| collection | MIT |
| description | Original manuscript December 17, 2009 |
| first_indexed | 2024-09-23T11:38:54Z |
| format | Article |
| id | mit-1721.1/80707 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:38:54Z |
| publishDate | 2013 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/807072022-10-01T04:59:53Z Branched Polymers and Hyperplane Arrangements Postnikov, Alexander Meszaros, Karola Massachusetts Institute of Technology. Department of Mathematics Postnikov, Alexander Original manuscript December 17, 2009 We generalize the construction of connected branched polymers and the notion of the volume of the space of connected branched polymers studied by Brydges and Imbrie (Ann Math, 158:1019–1039, 2003), and Kenyon and Winkler (Am Math Mon, 116(7):612–628, 2009) to any central hyperplane arrangement A A . The volume of the resulting configuration space of connected branched polymers associated to the hyperplane arrangement A A is expressed through the value of the characteristic polynomial of A A at 0. We give a more general definition of the space of branched polymers, where we do not require connectivity, and introduce the notion of q-volume for it, which is expressed through the value of the characteristic polynomial of A A at −q − q . Finally, we relate the volume of the space of branched polymers to broken circuits and show that the cohomology ring of the space of branched polymers is isomorphic to the Orlik–Solomon algebra. National Science Foundation (U.S.) (Grant DMS 6923772) National Science Foundation (U.S.) (CAREER Award DMS 0504629) 2013-09-13T12:47:57Z 2013-09-13T12:47:57Z 2013-04 2012-11 Article http://purl.org/eprint/type/JournalArticle 0179-5376 1432-0444 http://hdl.handle.net/1721.1/80707 Mészáros, Karola, and Alexander Postnikov. “Branched Polymers and Hyperplane Arrangements.” Discrete & Computational Geometry 50, no. 1 (July 23, 2013): 22-38. https://orcid.org/0000-0002-3964-8870 en_US http://dx.doi.org/10.1007/s00454-013-9499-8 Discrete & Computational Geometry Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Postnikov, Alexander Meszaros, Karola Branched Polymers and Hyperplane Arrangements |
| title | Branched Polymers and Hyperplane Arrangements |
| title_full | Branched Polymers and Hyperplane Arrangements |
| title_fullStr | Branched Polymers and Hyperplane Arrangements |
| title_full_unstemmed | Branched Polymers and Hyperplane Arrangements |
| title_short | Branched Polymers and Hyperplane Arrangements |
| title_sort | branched polymers and hyperplane arrangements |
| url | http://hdl.handle.net/1721.1/80707 https://orcid.org/0000-0002-3964-8870 |
| work_keys_str_mv | AT postnikovalexander branchedpolymersandhyperplanearrangements AT meszaroskarola branchedpolymersandhyperplanearrangements |