• Goutam Mukherjee

Articles written in Proceedings – Mathematical Sciences

• Equivariant cobordism of Grassmann and flag manifolds

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

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

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.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019