Presentation Title

Simple Subknots

Faculty Mentor

Matthew Rathbun

Start Date

23-11-2019 8:45 AM

End Date

23-11-2019 9:30 AM

Location

258

Session

poster 2

Type of Presentation

Poster

Subject Area

physical_mathematical_sciences

Abstract

Take a shoelace, tangle it up, then glue the two ends together. Now, cut the whole mess into two pieces, straighten out one half into a U-shape, then reattach it to the other half. The resulting knot is simpler than the one you started out with. How simple can it be without being trivial? Here, we use some tools from topology, particularly Seifert surfaces as well as cut-and-paste arguments, to prove that the simplest nontrivial knot must be a twist knot.

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Nov 23rd, 8:45 AM Nov 23rd, 9:30 AM

Simple Subknots

258

Take a shoelace, tangle it up, then glue the two ends together. Now, cut the whole mess into two pieces, straighten out one half into a U-shape, then reattach it to the other half. The resulting knot is simpler than the one you started out with. How simple can it be without being trivial? Here, we use some tools from topology, particularly Seifert surfaces as well as cut-and-paste arguments, to prove that the simplest nontrivial knot must be a twist knot.