Question 1: (Contrast with the ________ for the plane.) | |||
|
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. | |||
|
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. | |||
|
Question 4: A particular homeomorphism is given by ________ the topological torus into R3 from the north pole of S3. | |||
|
Question 5:
What does the following picture show?![]()
|
|||||||||
|
Question 6: Instead of the product of n circles, they use the phrase to mean the ________ of n 2-dimensional tori. | |||
|
Question 7: An n-torus in this sense is an example of an n-dimensional compact ________. | |||
|
Question 8: Every ________ on the 2-torus can be represented as a two-sheeted cover of the 2-sphere. | |||
|
Question 9: Its surface has zero ________ everywhere. | |||
|
Question 10: ________, a torus is a closed surface defined as the product of two circles: S1 × S1. | |||
|
|