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• W2852204061 abstract "Considering a closed monotone Lagrangian submanifold <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L comma> <mml:semantics> <mml:mrow> <mml:mi>L</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>L,</mml:annotation> </mml:semantics> </mml:math> </inline-formula> we give, under some hypotheses, a lower bound on the intersection number of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=application/x-tex>L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with its image by a generic Hamiltonian isotopy. First for monotone Lagrangian submanifolds <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=application/x-tex>L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which are <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=bold upper K left-parenthesis pi comma 1 right-parenthesis> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>K</mml:mi> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>π<!-- π --></mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>mathbf {K}(pi ,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and, in particular, for monotone Lagrangian submanifolds with negative sectional curvature this bound is 1+<inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=beta 1 left-parenthesis upper L right-parenthesis period> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>β<!-- β --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>L</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>.</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>beta _{1}(L).</mml:annotation> </mml:semantics> </mml:math> </inline-formula> In more general cases the lower bound is weaker. We generalise some results previously obtained by L. Buhovsky in [J. Topol. Anal. 2 (2010), pp. 57–75] and P. Biran and O. Cornea in [Geom. Topol. 13 (2009), pp. 2881–2989]." @default.
• W2852204061 created "2018-07-19" @default.
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• W2852204061 date "2022-11-04" @default.
• W2852204061 modified "2023-10-18" @default.
• W2852204061 title "New lower bounds on the number of intersections of monotone Lagrangian submanifolds" @default.
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• W2852204061 doi "https://doi.org/10.1090/tran/7640" @default.
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