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On Morse-Bott degenerations with $ Crit(\pi) \simeq\mathbb{C}P^k$ and Floer homology

Author: Yochay Jerby
Journal: Proc. Amer. Math. Soc. 142 (2014), 3731-3740
MSC (2010): Primary 14D05, 53D40
Published electronically: July 21, 2014
MathSciNet review: 3251714
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Abstract: Morse-Bott fibrations generalize the class of Lefschetz fibrations, allowing for non-isolated singularities. A Morse-Bott degeneration is a Morse-Bott fibration $ \pi : X \rightarrow \mathbb{D}$ whose only singular value is $ 0 \in \mathbb{D}$. We show that Morse-Bott degenerations with $ Crit(\pi )=\mathbb{C}P^k$ for $ 0<k$ admit restrictions which are unique to the non-isolated case. These restrictions are obtained as an application of methods of Floer homology for monotone Lagrangian submanifolds.

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Yochay Jerby
Affiliation: Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, CH-2000 Neuchâtel, Switzerland

Received by editor(s): April 5, 2012
Received by editor(s) in revised form: October 11, 2012, and December 6, 2012
Published electronically: July 21, 2014
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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