The rank of a compact Lie group is equal to the dimension of the maximal one of these entities in G.
Lawson's conjecture states that one of these objects named for Clifford is the only one that is minimally embedded in S-3. The rank of a compact Lie group is equal to the dimension of the maximal one of these entities in G. The n-dimensional one of these entities is defined by finding the product space of n circles. Seven colors are required to color the surface of one of these entities, and the volume of one of these entities is equal to 2 pi squared times outer radius times inner radius squared. For 10 points, name this surface that is famously homotopic to a coffee cup, since both have a single hole, a surface of revolution generated by rotating a circle through an axis not intersecting and co-planar with it.
Lawson's conjecture states that one of these objects named for Clifford is the only one that is minimally embedded in S-3.
torus [prompt on "donut"]