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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1994 • Question 7

Question

Math 6510 • Differentiable Manifolds Fall 1994 • Question 7

Let \(X\) be a finite connected graph. Then the fundamental group \(\pi _1(X,x_0)\) is a free group with \(1-\chi (X)\) generators. (\(\chi \) is the Euler characteristic.)

Raw LaTeX

Let \(X\) be a finite connected graph. Then the fundamental group
\(\pi_1(X,x_0)\) is a free group with \(1-\chi(X)\) generators. (\(\chi\) is the Euler
characteristic.)

Topic Tags

Euler Characteristic and Lefschetz Fixed Point Theorem Free Groups, Graph Coverings, and Presentations Fundamental Groups Homotopy Groups