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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2016 • Question 12

Question

Math 6510 • Differentiable Manifolds Summer 2016 • Question 12

Find all cohomology and homology groups (with \(\mathbb {Z}\) coefficients) of a closed connected orientable 3-manifold \(M\) with \(\pi _1(M,m_0)=\mathbb {Z}^r\times G\) where \(G\) is a finite group.

Raw LaTeX

Find all cohomology and homology groups (with \(\Z\) coefficients) of a
closed connected orientable 3-manifold \(M\) with
\(\pi_1(M,m_0)=\Z^r\times G\) where \(G\) is a finite group.

Topic Tags

Cohomology and Cup Products Fundamental Groups Homology with Coefficients Orientability and Volume Forms