. TOPOLOGY QUALIFYING EXAMINATION Time: Three hours.
... (a) Compute the fundamental group of the space obtained by identifying the points x and y pictured above on the solid three hole torus. (b) Compute the fundamental group of the space obtained by identifying the points x and y on the surface of the three hole torus. 2. (a) Define the join (or product ...
... (a) Compute the fundamental group of the space obtained by identifying the points x and y pictured above on the solid three hole torus. (b) Compute the fundamental group of the space obtained by identifying the points x and y on the surface of the three hole torus. 2. (a) Define the join (or product ...
Topology Exam 1 Study Guide (A.) Know precise definitions of the
... (A.) Know precise definitions of the following terms topology topological space metric base for a topology metric space generating set for a topology continuous homeomorphism subspace topology product topology equivalence relation group quotient topology Hausdorff connected path connected cover comp ...
... (A.) Know precise definitions of the following terms topology topological space metric base for a topology metric space generating set for a topology continuous homeomorphism subspace topology product topology equivalence relation group quotient topology Hausdorff connected path connected cover comp ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.