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Knot theory: Quiz

  
  
  

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Question 1: A variant of the Alexander polynomial, the ________, is a polynomial in the variable z with integer coefficients (Lickorish 1997).
Alexander polynomialKnot theorySkein relationKnot polynomial

Question 2: The endless knot appears in Tibetan Buddhism, while the ________ have made repeated appearances in different cultures, often representing strength in unity.
UnlinkLink groupBorromean ringsBrunnian link

Question 3: Geometry lets us visualize what the inside of a knot or link complement looks like by imagining light rays as traveling along the ________ of the geometry.
Affine connectionMetric tensorGeneral relativityGeodesic

Question 4: A plethora of knot invariants have been invented since then, utilizing sophisticated tools such as quantum groups and ________.
Floer homologyDifferentiable manifoldClifford TaubesMichael Atiyah

Question 5: In ________, knot theory is the area of topology that studies mathematical knots.
MathematicsSet theoryMathematical logicGeometry

Question 6: The first major verification of this work was done in the 1960s by ________, who not only developed a new notation but also the Alexander–Conway polynomial (Conway 1970)(Doll & Hoste 1991).
Richard K. GuyBill GosperJohn Horton ConwayGlider (Conway's Life)

Question 7: The Conway notation for knots and links, named after ________, is based on the theory of tangles (Conway 1970).
Glider (Conway's Life)Bill GosperJohn Horton ConwayRichard K. Guy

Question 8: ________ exist to solve this problem, with the first given by Wolfgang Haken in the late 1960s (Hass 1998).
LogicAlgorithm characterizationsAlgorithmAlan Turing

Question 9: SnapPea's cusp view: the ________ complement from the perspective of an inhabitant living near the red component.
Borromean ringsUnlinkLink groupBrunnian link

Question 10: Well-known examples include the Jones and ________.
Skein relationKnot polynomialAlexander polynomialKnot theory
















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