Extension of Tight Contact Structures from Tori to Solid Tori
Vol. 9 (2002), No. 3, Page 521--543.
Adachi, Jiro
Extension of Tight Contact Structures from Tori to Solid Tori
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
We study tight contact structures on the solid torus $S^1 Ã D^2$. We construct contact structures on the solid torus depending only on the given characteristic foliations on its boundary torus $S^1 Ã \partial D^2$. 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