Question 1: (Contrast with the ________ for the plane.)  

Question 2: The cohomology ring H^{•}(T^{n},Z) can be identified with the ________ over the Zmodule Z^{n} 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 ntorus 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 R^{3} from the north pole of S^{3}.  

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 2dimensional tori.  

Question 7: An ntorus in this sense is an example of an ndimensional compact ________.  

Question 8: Every ________ on the 2torus can be represented as a twosheeted cover of the 2sphere.  

Question 9: Its surface has zero ________ everywhere.  

Question 10: ________, a torus is a closed surface defined as the product of two circles: S^{1} × S^{1}.  

