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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2004 • Question 7

Question

Math 6510 • Differentiable Manifolds Fall 2004 • Question 7

Let \(V\) be the vector field in the complex plane \(\mathbb {C}\) given by \[ V(z)=z^m \] for some \(m=1,2,\cdots \), where we use the standard identification \(T_z\mathbb {C}=\mathbb {C}\). Compute the index of \(V\) at the origin.

Raw LaTeX

Let \(V\) be the vector field in the complex plane \(\mathbb{C}\) given by
\[
  V(z)=z^m
\]
for some \(m=1,2,\cdots\), where we use the standard identification \(T_z\mathbb{C}=\mathbb{C}\).
Compute the index of \(V\) at the origin.

Topic Tags

Left-Invariant Vector Fields Vector Fields and Flows