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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Fall 2024 • Question 7

Question

Math 6520 • Algebraic Topology Fall 2024 • Question 7

Show that if \(f : S^n \to S^n\) has degree \(d\) then the induced map \(f^* : H^n(S^n;G) \to H^n(S^n;G)\) is multiplication by \(d\).

Raw LaTeX

Show that if \(f : S^n \to S^n\) has degree \(d\) then the induced map \(f^* : H^n(S^n;G) \to H^n(S^n;G)\)
is multiplication by \(d\).

Topic Tags

Cohomology and Cup Products Degree Theory