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UID:3ca298dd5ae3d485ca062efe2c434da5
CATEGORIES:Topology/Geometry Seminar
CREATED:20210406T132348
SUMMARY:Using surgery to study unknotting with a single twist
LOCATION:zoom link:  https://rutgers.zoom.us/j/96007672653?pwd=UkhZV0l0WWNVenFqY1FYd
 jVydkVyQT09
DESCRIPTION:Ohyama showed that any knot can be unknotted by performing two full twists,
  each on a set of parallel strands. We consider the question of whether or 
 not a given knot can be unknotted with a single full twist, and if so, what
  are the possible linking numbers associated to such a twist. It is observe
 d that if a knot can be unknotted with a single twist, then some surgery on
  the knot bounds a rational homology ball. Using tools such as classical in
 variants and invariants arising from Heegaard Floer theory, we give obstruc
 tions for a knot to be unknotted with a single twist of a given linking num
 ber. In this talk, I will discuss some of these obstructions, their implica
 tions (especially for alternating knots), many examples, and some unanswere
 d questions. This talk is based on joint work with Charles Livingston.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="margin: 0px; padding: 0px; border: 0px; font: inherit; vertical-a
 lign: baseline; color: inherit;">Ohyama showed that any knot can be unknott
 ed by performing two full twists, each on a set of parallel strands. We con
 sider the question of whether or not a given knot can be unknotted with a s
 ingle full twist, and if so, what are the possible linking numbers associat
 ed to such a twist. It is observed that if a knot can be unknotted with a s
 ingle twist, then some surgery on the knot bounds a rational homology ball.
  Using tools such as classical invariants and invariants arising from Heega
 ard Floer theory, we give obstructions for a knot to be unknotted with a si
 ngle twist of a given linking number. In this talk, I will discuss some of 
 these obstructions, their implications (especially for alternating knots), 
 many examples, and some unanswered questions. This talk is based on joint w
 ork with Charles Livingston.</p>
CONTACT:Samantha Allen (Dartmouth)
DTSTAMP:20260828T185711
DTSTART;TZID=America/New_York:20210413T155000
DTEND;TZID=America/New_York:20210413T165000
SEQUENCE:0
TRANSP:OPAQUE
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