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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Summer 2022 • Question 1

Question

Math 6520 • Algebraic Topology Summer 2022 • Question 1

Let \(W\) be the union of the three coordinate axes in \(\mathbb {R}^3\) and set \(X:=\mathbb {R}^2\setminus W\); thus \(X\) consists of points \((x,y,z)\) where none of the coordinates are zero. Compute \(\pi _1(X)\).

Raw LaTeX

Let \(W\) be the union of the three coordinate axes in \(\mathbb{R}^3\) and set \(X:=\mathbb{R}^2\setminus W\); thus \(X\) consists of points \((x,y,z)\)
where none of the coordinates are zero. Compute \(\pi_1(X)\).

Topic Tags

Fundamental Groups Homotopy Groups