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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Fall 2022 • Question 4

Question

Math 6520 • Algebraic Topology Fall 2022 • Question 4

Compute the homology groups of the cell complex obtained by identifying the sides of the polygon below as indicated:

Figure: a hexagon with boundary edges, in clockwise order starting at the top, labeled \(a^{-1}\), \(c\), \(b\), \(a\), \(c^{-1}\), and \(b^{-1}\), with arrows indicating the side identifications.

Raw LaTeX

Compute the homology groups of the cell complex obtained by identifying the sides of the polygon below as
indicated:

Figure: a hexagon with boundary edges, in clockwise order starting at the top, labeled
\(a^{-1}\), \(c\), \(b\), \(a\), \(c^{-1}\), and \(b^{-1}\), with arrows indicating the side identifications.

Topic Tags

CW Complexes and Cell Attachments Cellular Homology Homology with Coefficients Relative Homology and Long Exact Sequences