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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Fall 2023 • Question 3

Question

Math 6520 • Algebraic Topology Fall 2023 • Question 3

Let \(\Sigma _g\) be the closed, orientable, genus-\(g\) surface. Show that \(\pi _1(\Sigma _2)\) contains \(\pi _1(\Sigma _4)\) as a normal subgroup.

Raw LaTeX

Let \(\Sigma_g\) be the closed, orientable, genus-\(g\) surface. Show that \(\pi_1(\Sigma_2)\)
contains \(\pi_1(\Sigma_4)\) as a normal subgroup.

Topic Tags

Fundamental Groups Homotopy Groups Surface Topology and Surface Groups