my question is fairly simple. I have been staring at this knot diagram for a while and cannot understand why its Conway Notation is 2 -2 2 -2 2 4 (according to Adam's The Knot Book). The way I understand it, a tangle is positive if the overstrand has a positive slope. However, all the strands between 2 and 4 have an overstrand with a negative slope as far as I can see. If that is not the case, could someone explain it to me? Thank you.
2026-03-26 16:04:00.1774541040
Conway Notation Question For a Knot Diagram
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1
The slope is positive or negative once the diagram is made into a "standard" diagram of a rational tangle closure. A way you can do that is to first identify what are the twist regions for this diagram:
Then inside each region, you can see whether it is a "vertical" or "horizontal" twist and figure out the slopes from that. Here's the same diagram, but distorted to make the slopes much clearer: