Well now. First, I'm embarrassed that I misspelled Dr. Piccirillo's name. Second, I apologize if I gave the impression that I had read and understood the proof. I only read and roughly understood the outline of the summary in Quanta. Perhaps it was silly of me to think I could glean any sense of Piccirillo's style from the description of her work. I was mostly admiring the structure of the "trace sibling" she constructed I wouldn't expect to understand her paper in Annals right off the bat; knot theory is an old discipline with deep traditions. But if I wanted to, I imagine I'd start by consulting her references, and if I couldn't understand them, recurse. This approach has worked okay for me before (though it has also failed, notably in anything having to do with algebraic topology). On Sat, May 23, 2020 at 11:14 PM Dan Asimov <dasimov@earthlink.net> wrote:
Yup. A p-sphere and a q-sphere can link when they're embedded disjoint from each other in (p+q+1)-dimensional space. (Even when p = q = 0.)
—Dan
Cris Moore wrote: ----- Thanks. I wonder where I got this 2d+1 thing… maybe I’m misremembering some other embedding theorem.
I do like the 5-dimensional construction of two linked 2-spheres, though, assuming I got that right. -----
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