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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2010 • Question 16

Question

Math 6510 • Differentiable Manifolds Spring 2010 • Question 16

Give an example of a connected cell complex \(X\) such that \(H_k(X;\mathbb {Z})=0\) for all \(k>0\) but \(\pi _1(X)\ne \{1\}\). You do not have to verify the second claim, but you should argue the first.

Raw LaTeX

Give an example of a connected cell complex \(X\) such that \(H_k(X;\Z)=0\)
for all \(k>0\) but \(\pi_1(X)\ne\{1\}\). You do not have to verify the second claim,
but you should argue the first.

Topic Tags

CW Complexes and Cell Attachments Fundamental Groups Homology with Coefficients Homotopy Groups