• Goutam Mukherjee

      Articles written in Proceedings – Mathematical Sciences

    • Equivariant cobordism of Grassmann and flag manifolds

      Goutam Mukherjee

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      We consider certain natural (ℤ2)n actions on real Grassmann and flag manifolds andS1 actions on complex Grassmann manifolds with finite stationary point sets and determine completely which of them bound equivariantly.

    • Bredon cohomology of cyclic geometric realization ofG-cyclic sets

      Goutam Mukherjee Aniruddha C Naolekar

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      We define equivariant cyclic and Hochschild cohomology modules of a cyclic objectX in the category ofG-sets and relate them with the Bredon cohomologies of the cyclic geometric realization ¦X¦cy.

    • Nambu structures and associated bialgebroids

      SAMIK BASU SOMNATH BASU APURBA DAS GOUTAM MUKHERJEE

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      We investigate higher-order generalizations of well known results for Liealgebroids and bialgebroids. It is proved that $n$-Lie algebroid structures correspond to $n$-ary generalization of Gerstenhaber algebras and are implied by $n$-ary generalization of linear Poisson structures on the dual bundle. A Nambu–Poisson manifold (of order $n$ > 2) gives rise to a special bialgebroid structure which is referred to as a weak Lie–Filippov bialgebroid (of order $n$). It is further demonstrated that such bialgebroids canonically induce a Nambu–Poisson structure on the base manifold. Finally, the tangent space of a Nambu Lie group gives an example of a weak Lie–Filippov bialgebroid over a point.

    • Nambu structures on Lie algebroids and their modular classes

      APURBA DAS SHILPA GONDHALI GOUTAM MUKHERJEE

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      We introduce the notion of the modular class of a Lie algebroid equipped with a Nambu structure. In particular, we recover the modular class of a Nambu-Poisson manifold $M$ with its Nambu tensor $\Lambda$ as the modular class of the tangent Lie algebroid $TM$ with Nambu structure $\Lambda$. We show that many known properties of the modular class of a Nambu-Poisson manifold and that of a Lie algebroid extend to the setting of a Lie algebroid with Nambu structure. Finally, we prove that for a large class of Nambu-Poisson manifolds considered as tangent Lie algebroids with Nambu structures, the associated modular classes are closely related to Evens-Lu-Weinstein modular classes of Lie algebroids.

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