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Torus: Quiz


Question 1: (Contrast with the ________ for the plane.)
Graph theoryFour color theoremGraph coloringPetersen graph

Question 2: The cohomology ring H(Tn,Z) can be identified with the ________ over the Z-module Zn whose generators are the duals of the n nontrivial cycles.
Clifford algebraRepresentation theoryVector spaceExterior algebra

Question 3: The classification theorem for surfaces states that every compact connected surface is either a sphere, an n-torus with n > 0, or the connected sum of n ________ (that is, projective planes over the real numbers) with n > 0.
Projective geometryFinite geometryProjective planeProjective space

Question 4: A particular homeomorphism is given by ________ the topological torus into R3 from the north pole of S3.
ManifoldStereographic projectionLambert azimuthal equal-area projectionConformal map

Question 5: What does the following picture show?

  The configuration space of 2 not necessarily distinct points on the circle is the orbifold quotient of the 2-torus, T2 / S2, which is the Möbius strip.
  This construction shows the torus divided into the maximum of seven regions, every one of which touches every other.
  The configuration space of 3 not necessarily distinct points on the circle, T3 / S3, is the above orbifold.
  A triple torus

Question 6: Instead of the product of n circles, they use the phrase to mean the ________ of n 2-dimensional tori.
ManifoldFiber bundleSurfaceConnected sum

Question 7: An n-torus in this sense is an example of an n-dimensional compact ________.
GeometryManifoldDifferentiable manifoldDifferential geometry

Question 8: Every ________ on the 2-torus can be represented as a two-sheeted cover of the 2-sphere.
Cartan connectionConformal geometryLie groupMöbius transformation

Question 9: Its surface has zero ________ everywhere.
Second fundamental formMean curvatureRicci curvatureGaussian curvature

Question 10: ________, a torus is a closed surface defined as the product of two circles: S1 × S1.
ManifoldAlgebraic topologyMathematicsTopology


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