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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2001 • Question 11

Question

Math 6510 • Differentiable Manifolds Fall 2001 • Question 11

Let \(M\) be a nonempty compact manifold, smooth or triangulated (you can make a choice). Show that \(M\) does not admit a retraction to its boundary.

Raw LaTeX

Let \(M\) be a nonempty compact manifold, smooth or triangulated (you can make a
choice). Show that \(M\) does not admit a retraction to its boundary.

Topic Tags

Homotopy Equivalence, Retracts, and Contractibility Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds