Algebraic varieties named for this shape are subject to the orbit–cone correspondence and can be constructed from fans. For knots named for this shape, “x-to-the-p equals y-to-the-q” is a relation of the knot group. “R-squared” quotient “Z-squared” is isomorphic to this surface, which has “Z-cross-Z” as its fundamental group. This surface can be obtained by gluing each pair of opposite edges of the unit square in the same direction. This orientable surface with Euler characteristic zero is the Cartesian product of two circles. Depending on orientation, either a Klein bottle or this genus-one surface is formed by joining the circular ends of a cylinder. For 10 points, the surface of a coffee cup is topologically equivalent to what single-holed surface shaped like a doughnut? ■END■
ANSWER: torus [or 2-torus; accept toric varieties; accept torus knots]
<Editors, Other Science>
= Average correct buzz position