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Hyperbolic lagrangian in a symplectic $6$-manifold
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Is there an example of a closed symplectic $6$-manifold and a closed lagrangian sub-manifold, which is diffeomorphic to a hyperbolic $3$-manifold?
symplectic-geometry
asked Jul 20 at 15:51
Nick L
7459
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up vote
4
down vote
favorite
Is there an example of a closed symplectic $6$-manifold and a closed lagrangian sub-manifold, which is diffeomorphic to a hyperbolic $3$-manifold?
symplectic-geometry
asked Jul 20 at 15:51
Nick L
7459
Could you clarify what do you mean by "closed" ? I interpret it as "compact without boundaries" but a compact submanifold can't be hyperbolic.
– Nicolas Hemelsoet
Jul 24 at 11:37
Yeah, I mean compact without boundary. Please could you explain why a compact sub-manifold cannot be hyperbolic?
– Nick L
Jul 24 at 12:50
Sorry this is wrong, I was thinking to something else.
– Nicolas Hemelsoet
Jul 24 at 13:31
You might wish to add a few tags to your question. The (symplectic-geometry) tag is not the most watched, and it is rather more symplectic geometry oriented than symplectic topology oriented, your question belonging to the latter field. Moreover my (probably exaggerated) impression is that 3-manifolds are not so well-known to many symplectic topologists. People in differential geometry/topology or in complex/kaehler geometry might be more capable of producing an example or a counter-argument, so I would advice that you try to reach them.
– Jordan Payette
Jul 28 at 16:52
add a comment |Â
up vote
4
down vote
favorite
up vote
4
down vote
favorite
Is there an example of a closed symplectic $6$-manifold and a closed lagrangian sub-manifold, which is diffeomorphic to a hyperbolic $3$-manifold?
symplectic-geometry
asked Jul 20 at 15:51
Nick L
7459
Is there an example of a closed symplectic $6$-manifold and a closed lagrangian sub-manifold, which is diffeomorphic to a hyperbolic $3$-manifold?
symplectic-geometry
asked Jul 20 at 15:51
Nick L
7459
asked Jul 20 at 15:51
Nick L
7459
asked Jul 20 at 15:51
Nick L
7459
asked Jul 20 at 15:51
Nick L
7459
7459
Could you clarify what do you mean by "closed" ? I interpret it as "compact without boundaries" but a compact submanifold can't be hyperbolic.
– Nicolas Hemelsoet
Jul 24 at 11:37
Yeah, I mean compact without boundary. Please could you explain why a compact sub-manifold cannot be hyperbolic?
– Nick L
Jul 24 at 12:50
Sorry this is wrong, I was thinking to something else.
– Nicolas Hemelsoet
Jul 24 at 13:31
You might wish to add a few tags to your question. The (symplectic-geometry) tag is not the most watched, and it is rather more symplectic geometry oriented than symplectic topology oriented, your question belonging to the latter field. Moreover my (probably exaggerated) impression is that 3-manifolds are not so well-known to many symplectic topologists. People in differential geometry/topology or in complex/kaehler geometry might be more capable of producing an example or a counter-argument, so I would advice that you try to reach them.
– Jordan Payette
Jul 28 at 16:52
add a comment |Â
Could you clarify what do you mean by "closed" ? I interpret it as "compact without boundaries" but a compact submanifold can't be hyperbolic.
– Nicolas Hemelsoet
Jul 24 at 11:37
Yeah, I mean compact without boundary. Please could you explain why a compact sub-manifold cannot be hyperbolic?
– Nick L
Jul 24 at 12:50
Sorry this is wrong, I was thinking to something else.
– Nicolas Hemelsoet
Jul 24 at 13:31
You might wish to add a few tags to your question. The (symplectic-geometry) tag is not the most watched, and it is rather more symplectic geometry oriented than symplectic topology oriented, your question belonging to the latter field. Moreover my (probably exaggerated) impression is that 3-manifolds are not so well-known to many symplectic topologists. People in differential geometry/topology or in complex/kaehler geometry might be more capable of producing an example or a counter-argument, so I would advice that you try to reach them.
– Jordan Payette
Jul 28 at 16:52
Could you clarify what do you mean by "closed" ? I interpret it as "compact without boundaries" but a compact submanifold can't be hyperbolic.
– Nicolas Hemelsoet
Jul 24 at 11:37
Could you clarify what do you mean by "closed" ? I interpret it as "compact without boundaries" but a compact submanifold can't be hyperbolic.
– Nicolas Hemelsoet
Jul 24 at 11:37
Yeah, I mean compact without boundary. Please could you explain why a compact sub-manifold cannot be hyperbolic?
– Nick L
Jul 24 at 12:50
Yeah, I mean compact without boundary. Please could you explain why a compact sub-manifold cannot be hyperbolic?
– Nick L
Jul 24 at 12:50
Sorry this is wrong, I was thinking to something else.
– Nicolas Hemelsoet
Jul 24 at 13:31
Sorry this is wrong, I was thinking to something else.
– Nicolas Hemelsoet
Jul 24 at 13:31
You might wish to add a few tags to your question. The (symplectic-geometry) tag is not the most watched, and it is rather more symplectic geometry oriented than symplectic topology oriented, your question belonging to the latter field. Moreover my (probably exaggerated) impression is that 3-manifolds are not so well-known to many symplectic topologists. People in differential geometry/topology or in complex/kaehler geometry might be more capable of producing an example or a counter-argument, so I would advice that you try to reach them.
– Jordan Payette
Jul 28 at 16:52
You might wish to add a few tags to your question. The (symplectic-geometry) tag is not the most watched, and it is rather more symplectic geometry oriented than symplectic topology oriented, your question belonging to the latter field. Moreover my (probably exaggerated) impression is that 3-manifolds are not so well-known to many symplectic topologists. People in differential geometry/topology or in complex/kaehler geometry might be more capable of producing an example or a counter-argument, so I would advice that you try to reach them.
– Jordan Payette
Jul 28 at 16:52
add a comment |Â
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Could you clarify what do you mean by "closed" ? I interpret it as "compact without boundaries" but a compact submanifold can't be hyperbolic.
– Nicolas Hemelsoet
Jul 24 at 11:37
Yeah, I mean compact without boundary. Please could you explain why a compact sub-manifold cannot be hyperbolic?
– Nick L
Jul 24 at 12:50
Sorry this is wrong, I was thinking to something else.
– Nicolas Hemelsoet
Jul 24 at 13:31
You might wish to add a few tags to your question. The (symplectic-geometry) tag is not the most watched, and it is rather more symplectic geometry oriented than symplectic topology oriented, your question belonging to the latter field. Moreover my (probably exaggerated) impression is that 3-manifolds are not so well-known to many symplectic topologists. People in differential geometry/topology or in complex/kaehler geometry might be more capable of producing an example or a counter-argument, so I would advice that you try to reach them.
– Jordan Payette
Jul 28 at 16:52