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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1994 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 1994 • Question 3

\[ \pi _k\left (\underbrace {S^1\times \cdots \times S^1}_{n\ \mathrm {times}},x_0\right ) = \begin {cases} \mathbb {Z}^n, & \text {if } k=1,\\ 0, & \text {if } k>1. \end {cases} \]

Raw LaTeX

\[
  \pi_k\left(\underbrace{S^1\times\cdots\times S^1}_{n\ \mathrm{times}},x_0\right)
  =
  \begin{cases}
    \mathbb{Z}^n, & \text{if } k=1,\\
    0, & \text{if } k>1.
  \end{cases}
\]

Topic Tags

Fundamental Groups