06-1350/Class Notes for Tuesday October 10
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Question 1. Can you embed a trinion (a.k.a. a sphere with three holes, a pair of pants, or a band theta graph) in so that each boundary component would be unknotted yet each pair of boundary components would be knotted? How about, so that at least one pair of boundary components would be knotted?
Question 2. Suppose two trinions and are knotted so that the pushforwards and are equal for any link which is "drawn" on the parameter space of and . Does it follow that and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma_2} are equivalent?
Question 3. A trinion is embedded in so that its boundary is the trivial 3-component link. Does it follow that is trivial?
Question 4. A trinion is embedded in so that its "strapped boundary" is equivalent to the strapped boundary of the trivially embedded trinion. Does it follow that is trivial?