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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2012 • Question 8

Question

Math 6510 • Differentiable Manifolds Spring 2012 • Question 8

Let \(X\) be the space obtained from the circle \(S^1\) by attaching two 2-cells, one with degree 2 attaching map, and the other with degree 4 attaching map. What is the cardinality of the fundamental group of \(X\)? If you use van Kampen’s theorem, state it.

Raw LaTeX

Let \(X\) be the space obtained from the circle \(S^1\) by attaching two
2-cells, one with degree 2 attaching map, and the other with degree 4 attaching
map. What is the cardinality of the fundamental group of \(X\)? If you use van
Kampen's theorem, state it.

Topic Tags

CW Complexes and Cell Attachments Fundamental Groups Homotopy and Degree on Manifolds Seifert-van Kampen Theorem