https://doi.org/10.1140/epjb/s10051-025-00942-1
Regular Article - Statistical and Nonlinear Physics
The space writhes and signatures of polymer knots
1
School of Mathematics and Physics, University of Queensland, Brisbane, Australia
2
Department of Mathematical Sciences, Smith College, Northampton, USA
3
Department of Physics and Astronomy, California State University, Long Beach, Long Beach, USA
Received:
28
January
2025
Accepted:
26
April
2025
Published online:
8
May
2025
The space writhe of a knot is a property of its three-dimensional embedding that contains information about its underlying topology, but the correspondence between space writhe and other topological invariants is not fully understood. We perform Langevin dynamics simulations of knotted semi-flexible polymers and measure their ensemble average space writhe. We show that for all knots up to 10 crossings, alternating and non-alternating, the average space writhe is almost equal to that of the tightest known configuration of the same knot, with minor differences. Using this equivalence, we show that for more complex knots with up to 38 crossings, the average space writhe is strongly correlated with the signature of the knot. This establishes that the connection between signature and space writhe holds at larger crossing numbers.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-025-00942-1.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
