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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Fall 2022 • Question 2

Question

Math 6520 • Algebraic Topology Fall 2022 • Question 2

Draw a picture of a covering space of \(S^1\vee S^1\) whose fundamental group is the normal subgroup of \(\pi _1(S^1\vee S^1,*)\) generated by \(a^2\), \(b^2\), and \((ab)^2\), and prove your covering space is the correct one.

Raw LaTeX

Draw a picture of a covering space of \(S^1\vee S^1\) whose fundamental group is the normal subgroup of \(\pi_1(S^1\vee S^1,*)\)
generated by \(a^2\), \(b^2\), and \((ab)^2\), and prove your covering space is the correct one.

Topic Tags

Classification of Covering Spaces Covering Spaces Fundamental Groups Homotopy Groups