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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Fall 2022 • Question 5

Question

Math 6520 • Algebraic Topology Fall 2022 • Question 5

Let \(M\) be closed, connected, 5-manifold such that \(\pi _1(M)\cong \mathbb {Z}/7\) and \(H_2(M)=\mathbb {Z}\). Compute all homology and cohomology groups of \(M\) with \(\mathbb {Z}\)-coefficients.

Raw LaTeX

Let \(M\) be closed, connected, 5-manifold such that \(\pi_1(M)\cong\mathbb{Z}/7\) and \(H_2(M)=\mathbb{Z}\). Compute all homology and
cohomology groups of \(M\) with \(\mathbb{Z}\)-coefficients.

Topic Tags

Cohomology and Cup Products Fundamental Groups Homology with Coefficients Homotopy Groups