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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1995 • Question 17

Question

Math 6510 • Differentiable Manifolds Fall 1995 • Question 17

Let \(M\) be a differentiable manifold, \(\omega \) a closed \(p\)-form satisfying \[ \int _c \omega =0 \] for all smooth \(p\)-cycles \(c\). Prove \(\omega \) is exact.

Raw LaTeX

Let \(M\) be a differentiable manifold, \(\omega\) a closed \(p\)-form
satisfying
\[
  \int_c \omega=0
\]
for all smooth \(p\)-cycles \(c\). Prove \(\omega\) is exact.

Topic Tags

Differential Forms and Exterior Calculus Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds