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M. Alessandro Ferrari
M. Alessandro Ferrari
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It is a well-known fact that $S^2 \times S^1$ can be obtained by $0$-surgery on unknot.

What about the $-1$ surgery$(-1)$-surgery on $S^2 \times S^1$? It seems the resulting manifold, say $W$, bounds contractible manifold.

But I cannot prove it yet or refutes my argument. Any help will be appreciated.

It is a well-known fact that $S^2 \times S^1$ can be obtained by $0$-surgery on unknot.

What about the $-1$ surgery on $S^2 \times S^1$? It seems the resulting manifold, say $W$, bounds contractible manifold.

But I cannot prove it yet or refutes my argument. Any help will be appreciated.

It is a well-known fact that $S^2 \times S^1$ can be obtained by $0$-surgery on unknot.

What about the $(-1)$-surgery on $S^2 \times S^1$? It seems the resulting manifold, say $W$, bounds contractible manifold.

But I cannot prove it yet or refutes my argument. Any help will be appreciated.

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M. Alessandro Ferrari
M. Alessandro Ferrari
  • 93
  • 5

Integral surgery on $S^2 \times S^1$

It is a well-known fact that $S^2 \times S^1$ can be obtained by $0$-surgery on unknot.

What about the $-1$ surgery on $S^2 \times S^1$? It seems the resulting manifold, say $W$, bounds contractible manifold.

But I cannot prove it yet or refutes my argument. Any help will be appreciated.