Knot theory news:
Mark Brittenham & Susan Hermiller: 'Unknotting number is not additive under connected sum': https://arxiv.org/abs/2506.24088
If you have a knot tied in a loop of string then the 'unknotting number' is the number of times you would need to pass the string through itself in order to untie it. It was an old conjecture that the unknotting number of two knots tied in the same piece of string was just the sum of the unknotting numbers of the two knots individually. But this result shows that it can be easier to undo two knots when they're both tied in the same loop than it would be if they were each tied in separate loops.
#Math #Maths #Mathematics #KnotTheory
Oscar Cunningham
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2025-07-01 13:18:56 UTC
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2025-07-01 13:18:56 UTCEvent JSON
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"content": "Knot theory news:\n\nMark Brittenham \u0026 Susan Hermiller: 'Unknotting number is not additive under connected sum': https://arxiv.org/abs/2506.24088\n\nIf you have a knot tied in a loop of string then the 'unknotting number' is the number of times you would need to pass the string through itself in order to untie it. It was an old conjecture that the unknotting number of two knots tied in the same piece of string was just the sum of the unknotting numbers of the two knots individually. But this result shows that it can be easier to undo two knots when they're both tied in the same loop than it would be if they were each tied in separate loops.\n\n#Math #Maths #Mathematics #KnotTheory",
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