Rigidity of ADC contact structures
We show by a counter example that any Liouville filling of a ADC closed contact manifold does not have isomorphic integral cohomologies.
math.SG↗
arXiv subjects
Sauvik Mukherjee
Publications and source records attributed to Sauvik Mukherjee.
Characterizing Regular Lagrangians by Lefschetz Fibration
We prove that the existence of regular Lagrangians can be given by existence of Weinstein Lefschetz fibrations with an hypothesis.
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Weinstein Homotopies
We give a partial answer to a question asked by Eliashberg in one of his recent papers.
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Regular Symplectic Foliations on Closed manifolds
In this paper we prove h-principal for regular Symplectic Foliations on Closed manifolds.
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Poisson Structures On Closed Manifolds
We prove an h-principle for poisson structures on closed manifolds.
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Thurston's h-principle and Flexibility of Poisson Structures
We prove an analogue of Thurston's h-principle for $2$-dimensional foliations on manifolds of dimension bigger or equal to $4$, in the presence of a fiber-wise non-degenerate $2$-form. This helps us understand the flexibility of rank $2$ regular Poisson structures on open manifolds with dimension bigger or equal to $4$ and it also helps us understand the flexibility of Poisson structures (not regular) on closed $4$-manifolds.
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Seifert's conjecture for almost symplectic foliations
We disproving Seifert's conjecture for almost symplectic foliations with co-dimension bigger or equal to 3.
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On existence of non-compact exact lagrangian cobordism
We prove an existence result for exact lagrangian cobordisms between closed legendrians.
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Symplectic A-directed Immersions
We derive a symplectic analogue of A-directed immersion theorem.
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Homotopy classification of contact foliations on an open contact manifold
We give a complete classification of foliations on open contact manifolds whose leaves are contact submanifolds of the ambient manifold. The results are analogues of Haefliger's classification of foliations on open manifold.
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Foliations with geometric structures
A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures. The thesis consists of two parts. In the first part we classify foliations on open manifolds whose leaves are either locally conformal symplectic or contact manifolds. These foliations can be described by some higher geometric structures - namely the Poisson and the Jacobi structures. In the second part of the thesis, we consider foliations on open contact manifolds whose leaves are contact submanifolds of the ambient space. Theory of h-principle plays the central role in deriving the main results of the thesis. It is a theory rich in topological techniques to solve partial differential relations which arise in connection with topology and geometry. All the geometric structures mentioned above satisfy some differential conditions and that brings us into the realm of the h-principle theory.
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On Existence of Regular Jacobi Structures
We prove $h$-principle for locally conformal symplectic foliations and contact foliations on open manifolds. We interpret the result on $h$ principle of contact foliations in terms of the regular Jacobi structures.
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