Open book structures on $(n-1)$-connected $(2n+1)$-manifolds

J. Math. Sci. Univ. Tokyo
Vol. 13 (2006), No. 4, Page 439--523.

Neto, Oziride Manzoli; Massago, Sadao ;Saeki, Osamu
Open book structures on $(n-1)$-connected $(2n+1)$-manifolds
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We completely classify simple open book structures on $(n-1)$-connected closed $(2n+1)$-dimensional manifolds for $n\ge 4$, $n\ne 7$, and on $(n-1)$-connected rational homology $(2n+1)$-spheres for $n=3,7$, using their algebraic topological invariants. This generalizes some known results about the classification of fibered knots in spheres and the existence of open book structures on manifolds. We also give applications and examples so as to show the effectiveness of our classification.

Keywords: Fibered knot, isotopy of embeddings, Milnor fibration, open book, rational Seifert form, spinnable structure

Mathematics Subject Classification (2000): Primary 57Q45; Secondary 57R40
Mathematical Reviews Number: MR2306217

Received: 2003-10-30