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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2004 • Question 19

Question

Math 6510 • Differentiable Manifolds Fall 2004 • Question 19

Let \(X\) be a connected CW-complex obtained by attaching an \((n+2)\)-dimensional cell to an \(n\)-dimensional CW-complex \(A\). What is the smallest possible dimension \(k\) where \(\pi _k(X)\) is not isomorphic to \(\pi _k(A)\)?

Raw LaTeX

Let \(X\) be a connected CW-complex obtained by attaching an \((n+2)\)-dimensional
cell to an \(n\)-dimensional CW-complex \(A\). What is the smallest possible dimension \(k\)
where \(\pi_k(X)\) is not isomorphic to \(\pi_k(A)\)?

Topic Tags

CW Complexes and Cell Attachments Fundamental Groups