|© | Dror Bar-Natan: Classes: 2004-05: Math 1300Y - Topology:||(79)||
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Math 1300Y Students: Make sure to write ``1300Y'' in the course field on the exam notebook. Solve one of the two problems in part A and three of the four problems in part B. Each problem is worth 25 points. If you solve more than the required 1 in 2 and 3 in 4, indicate very clearly which problems you want graded; otherwise random ones will be left out at grading and they may be your best ones! You have an hour and 50 minutes. No outside material other than stationary is allowed.
Math 427S Students: Make sure to write ``427S'' in the course field on the exam notebook. Solve the four problems in part B, do not solve anything in part A. Each problem is worth 25 points. You have an hour and 50 minutes. No outside material other than stationary is allowed.
Problem 1. Let be a group with product .
Problem 3. Let be a connected, locally connected and semi-locally simply connected topological space with basepoint .
Problem 5. Let and be disjoint topological spaces with basepoints and , respectively. Assume also that has a neighborhood that deformation retracts (i.e., contracts) to and likewise that has a neighborhood that contracts to . Recall that the wedge sum is . What is the relationship between the homologies (reduced or not, your choice) of , and ? Prove your assertions. (Hint: it is a good idea to excise the ``linkage point'' ).
Problem 6. A 3-dimensional -complex is defined by