by Staff Writers
Seoul, South Korea (SPX) Jul 10, 2017
From bow ties and shoelaces to sailing boats and climbing ropes, knots are not only very useful for our daily lives, but for mathematics too. IBS researchers from the Center for Geometry and Physics, within the Institute for Basic Science (IBS) reported a new mathematical operation to catalog a special kind of mathematical knots, known as Legendrian singular knots. Their study, accepted by the Journal of Symplectic Geometry, deals with knots that go well beyond the annoying entanglement of headphone wires.
Why care about knots?
Making perfect knots on ties and quick knots on shoes are good skills to have, but why are mathematicians so interested in knots? It turns out that beyond being an intriguing mathematical curiosity, knots are also at the root of understanding our universe. Interestingly, classifying knots is crucial to study complex 3D spaces, like our universe.
"No one has circumnavigated the universe, like Magellan did on Earth, so we don't know its shape. Space travel aside, mathematicians are investigating knots to provide a tentative list of all the possible shapes of the universe," explains KIM Seonhwa, one of the authors of the study.
His colleague HEE An Byung adds: "There could be an uncountably infinite number of possible 3D spaces. At the moment, the shape of some patches of our universe are clarified, but we miss the overall structure, that's where knot theory can help us."
The challenge of classifying knots
Several rules for differentiating knots are available, but for this study, IBS mathematicians focused on a special type of knots, called Legendrian singular knots (LSKs), which are much harder to classify. LSKs belong to a branch of mathematics known as symplectic geometry, which is one of the most important fields in modern mathematics and physics.
The research team devised a new operation, called 'singular connected sum', to investigate and distinguish LSKs. As applicable rules to classify other types of knots, namely Legendrian knots and singular knots, do not work with LSKs, this study represents an important step forward in knot theory.
"It looked like there was a huge number of possible situations, making LSKs very hard to classify. Thanks to this new operation and its properties, we demonstrated the number of possibilities is not as horrible as it looked.
Furthermore, we made an example which shows that LSKs are more than the combination of Legendrian knots and singular knots," points out BAE Youngjin, another mathematician involved in the study.
The study is the result of a collaboration among three researchers involved with different fields of mathematics. This fits in the spirit of the Center for Geometry and Physics, which encourages the blending of different lines of research.
A deeper analysis of the singular connected sum operation is already underway. It aims to explore even more elaborate objects of symplectic geometry; the Legendrian spatial graphs, and hopefully help us to understand the fascinating possibilities of 3D spaces, including our universe.
Melbourne, Australia (SPX) Jul 07, 2017
In the harshest of environments in far-east Russia, Monash scientists have played a leading role in the discovery of a new mineral, which could revolutionise the future of the mining industry. The mineral - Nataliyamalikite - is new, and did not exist before, explains Professor Joel Brugger, the lead author in a recently published paper in American Mineralogist. It contains thallium, ... read more
Institute for Basic Science
Space Technology News - Applications and Research
|The content herein, unless otherwise known to be public domain, are Copyright 1995-2017 - Space Media Network. All websites are published in Australia and are solely subject to Australian law and governed by Fair Use principals for news reporting and research purposes. AFP, UPI and IANS news wire stories are copyright Agence France-Presse, United Press International and Indo-Asia News Service. ESA news reports are copyright European Space Agency. All NASA sourced material is public domain. Additional copyrights may apply in whole or part to other bona fide parties. All articles labeled "by Staff Writers" include reports supplied to Space Media Network by industry news wires, PR agencies, corporate press officers and the like. Such articles are individually curated and edited by Space Media Network staff on the basis of the report's information value to our industry and professional readership. Advertising does not imply endorsement, agreement or approval of any opinions, statements or information provided by Space Media Network on any Web page published or hosted by Space Media Network. Privacy Statement|