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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2009 • Question 13

Question

Math 6510 • Differentiable Manifolds Fall 2009 • Question 13
Using \(\Delta\)-homology, compute homology and cohomology (with \(\mathbb{Z}\) coefficients) of the following space (solid square and triangle with identifications as indicated). ![Diagram from GeomTopF2009](../../Exams-pre-2020/Geometry-Topology-Accessible/GeomTopF2009-diagram-13.png)

Raw LaTeX

Using \(\Delta\)-homology, compute homology and cohomology (with \(\Z\)
coefficients) of the following space (solid square and triangle with identifications
as indicated).
\begin{center}
  \includegraphics[
    alt={Solid square and triangle side-identification diagram from the original exam.},
    width=0.32\textwidth
  ]{GeomTopF2009-diagram-13.png}
\end{center}

Topic Tags

Cohomology and Cup Products Free Groups, Graph Coverings, and Presentations Homology with Coefficients de Rham Cohomology