Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2017 • Question 10

Question

Math 6510 • Differentiable Manifolds Summer 2017 • Question 10

Let \(n,k\in \N \) with \(n\ge 2\). Suppose \(f:\mathbb {R}\mathrm {P}^n\to T^k\) is continuous. Determine \[ f_*:H_m(\mathbb {R}\mathrm {P}^n)\to H_m(T^k) \] for all \(m\).

Raw LaTeX

Let \(n,k\in\N\) with \(n\ge2\). Suppose \(f:\RP^n\to T^k\) is continuous.
Determine
\[
  f_*:H_m(\RP^n)\to H_m(T^k)
\]
for all \(m\).

Topic Tags

Real Projective Spaces