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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2005 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 2005 • Question 3

Let \(M\) be a nonempty compact manifold with empty boundary. Prove that there is no compact manifold \(W\subset M\times M\) whose boundary \(\partial W\) is the diagonal \(\Delta =\{(x,x)\in M\times M\}\).

Raw LaTeX

Let \(M\) be a nonempty compact manifold with empty boundary. Prove that there is
no compact manifold \(W\subset M\times M\) whose boundary \(\partial W\) is the diagonal
\(\Delta=\{(x,x)\in M\times M\}\).

Topic Tags

Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds