Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2017 • Question 12

Question

Math 6510 • Differentiable Manifolds Spring 2017 • Question 12

Let \(M\) be a closed, orientable 3-manifold such that \[ H_1(M;\mathbb {Z})=\mathbb {Z}\oplus \mathbb {Z}_3. \] Calculate the remaining homology and cohomology groups for \(M\) with \(\mathbb {Z}\) coefficients.

Raw LaTeX

Let \(M\) be a closed, orientable 3-manifold such that
\[
  H_1(M;\Z)=\Z\oplus\Z_3.
\]
Calculate the remaining homology and cohomology groups for \(M\) with \(\Z\)
coefficients.

Topic Tags

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