Problem Sheet M

This sheet is based on Lectures 26 and 27.

• Problems 1-2 fill in gaps from Lecture 26.
• Problem 3 asks to compute the homology of the product of two even-dimensional projective spaces.
• Problem 4 gives three examples of spaces that have the same homology groups but that are not homotopy equivalent. This shows that singular homology is not a powerful enough to distinguish these spaces alone. This problem is meant to be an “exam style” question. 😈

🤓 Feel free to ask a question if you are stuck! 🤓