Extension of Tight Contact Structures from Tori to Solid Tori

J. Math. Sci. Univ. Tokyo
Vol. 9 (2002), No. 3, Page 521--543.

Adachi, Jiro
Extension of Tight Contact Structures from Tori to Solid Tori
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Abstract:
We study tight contact structures on the solid torus $S^1 × D^2$. We construct contact structures on the solid torus depending only on the given characteristic foliations on its boundary torus $S^1 × \partial D^2$. Then, it is shown that tight contact structures on the solid torus, which admit transverse meridian curves on its boundary torus with a self-linking number $-1$ are determined up to an isotopy by their characteristic foliations on its boundary torus.

Mathematics Subject Classification (2000): 57R17, 53D35
Mathematical Reviews Number: MR1930417

Received: 2001-02-13