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added 29 characters in body
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Chris Gerig
Chris Gerig
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For (3), here is a nice counterexample if we ignore contractibility (taken from an article from The American Mathematical Monthly):

http://www.jstor.org/stable/pdfplus/2695643.pdf

Hopefully someone can embed the image (Figure 13). It is two topologically distinct manifolds with the torus as a boundary... one being a solid [knot] torus, and the other being a 'cylinder' with a knotted inner-hole.

For (3), here is a nice counterexample (taken from an article from The American Mathematical Monthly):

http://www.jstor.org/stable/pdfplus/2695643.pdf

Hopefully someone can embed the image (Figure 13). It is two topologically distinct manifolds with the torus as a boundary... one being a solid [knot] torus, and the other being a 'cylinder' with a knotted inner-hole.

For (3), here is a nice counterexample if we ignore contractibility (taken from an article from The American Mathematical Monthly):

http://www.jstor.org/stable/pdfplus/2695643.pdf

Hopefully someone can embed the image (Figure 13). It is two topologically distinct manifolds with the torus as a boundary... one being a solid [knot] torus, and the other being a 'cylinder' with a knotted inner-hole.

Source Link
Chris Gerig
Chris Gerig
  • 17.5k
  • 2
  • 71
  • 116

For (3), here is a nice counterexample (taken from an article from The American Mathematical Monthly):

http://www.jstor.org/stable/pdfplus/2695643.pdf

Hopefully someone can embed the image (Figure 13). It is two topologically distinct manifolds with the torus as a boundary... one being a solid [knot] torus, and the other being a 'cylinder' with a knotted inner-hole.