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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2009 • Question 16

Question

Math 6510 • Differentiable Manifolds Fall 2009 • Question 16

Describe the procedure for computing (i.e. writing down a presentation of) the fundamental group of a cell complex with one 0-cell. Using this, show that \(\mathbb {C}P^n\) is simply connected and \(\pi _1(\mathbb {R}P^n)=\mathbb {Z}/2\mathbb {Z}\) for \(n\ge 2\).

Raw LaTeX

Describe the procedure for computing (i.e. writing down a presentation of)
the fundamental group of a cell complex with one 0-cell. Using this, show that
\(\mathbb{C}P^n\) is simply connected and
\(\pi_1(\mathbb{R}P^n)=\Z/2\Z\) for \(n\ge2\).

Topic Tags

CW Complexes and Cell Attachments Free Groups, Graph Coverings, and Presentations Fundamental Groups Homotopy Groups