Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2006 • Question 9

Question

Math 6510 • Differentiable Manifolds Fall 2006 • Question 9

Let \(X\) be the quotient space of \(S^2\) obtained by identifying the north and south poles to a single point. Carefully define a cell complex structure on \(X\) (including a description of attaching maps) and use this to compute \(\pi _1(X)\).

Raw LaTeX

Let \(X\) be the quotient space of \(S^2\) obtained by identifying the north and south
poles to a single point. Carefully define a cell complex structure on \(X\) (including a
description of attaching maps) and use this to compute \(\pi_1(X)\).

Topic Tags

CW Complexes and Cell Attachments Fundamental Groups Homotopy Groups