Dehn surgery on crosscap number two knots and projective planes

In the present paper, we will study the creation of projective planes by Dehn surgery on knots in the 3-sphere. It is shown that a projective plane cannot be created by Dehn surgery on a crosscap number two knot. As a corollary, we will prove that crosscap number two knots satisfy the projective space conjecture, which asserts that the projective 3-space cannot be obtained by Dehn surgery on a non-trivial knot in the 3-sphere.

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