Journal article
Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v 32(5), 2350032
Apr 2023
Abstract
A weave is the lift to the thickened Euclidean plane of a particular type of quadrivalent planar connected graph with an over or under crossing information to each vertex and such that the lifted components are non-intersecting simple open curves. In this paper, we introduce a formal topological definition of weaves as three-dimensional entangled structures and characterize the equivalence classes of doubly periodic untwisted (p,q)-weaves by introducing a new invariant, called crossing matrix. Finally, we suggest a combinatorial approach to classify this specific class of weaves by their crossing number.
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Details
- Title
- Classification of doubly periodic untwisted (p,q)-weaves by their crossing number and matrices
- Publication Details
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v 32(5), 2350032
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD; SINGAPORE
- Grant note
- We would like to thank A. Cheritat (IMT), T. Kechadi (UCD), and M. Evans and her group (U. Potsdam, T.U. Berlin) for their precious comments and advice during this study. This work is supported by a Research Fellowship from JST CREST Grant No. JPMJCR17J4 and Grant-in Aid for JSPS Fellows Number 22J13397.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Drexel University
- Web of Science ID
- WOS:000996510400001
- Scopus ID
- 2-s2.0-85161990321
- Other Identifier
- 991021861213904721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics