Hi, everyone:(adsbygoogle = window.adsbygoogle || []).push({});

I would appreciate any help with the following:

I am trying to refresh my knot theory--it's been a while. I am trying to answer

the following:

1) Every simple polygonal knot P in R^2 is trivial.:

I have tried to actually construct a homeomorphism h:R^3 -->R^3 , with

h|_P = S^1 , i.e., the restriction of the automorphism h to the poly. knot P gives

us S^1

I actually tried going in the opposite direction by creating a homeo. between a

polygonal knot P and S^1 (and seeing if I can extend it to h:R^3 -->R^3 ):

find a circle C going through the vertices of P (So that C an P are coplanar)

and then smoothly deform P to S^1. But I cannot see how to extend this to

an homeo. h:R^3 -->R^3 that restricts to this map.

2) Show there are no knotted quadrilateral nor pentagonal knots.

I have no clue here. Any Ideas.?.

Thanks.

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# Knots: Simple Closed Polygons are Trivial, there are no quadrilateral, pentagon knots

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