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STUDY ON CHOHOMOLOGY OF SUPERMANIFOLDS

Moslehuddin Ahmed .

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Abstract

In this present paper de Rham cohomology of graded manifolds, cohomology of graded differential forms and cohomology of DeWitt supermanifolds are studied. The structure of a G-supermanifold in general is not acyclic. So, the cohomology is defined via the complex of graded differential forms. This situation is investigated together with the graded Dolbeault cohomology of complex G-supermanifolds. A theorem is established that the structure sheaf of any DeWitt G-supermanifold is acyclic.

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In this present paper de Rham cohomology of graded manifolds, cohomology of graded differential forms and cohomology of DeWitt supermanifolds are studied. The structure of a G-supermanifold in general is not acyclic. So, the cohomology is defined via the complex of graded differential forms. This situation is investigated together with the graded Dolbeault cohomology of complex G-supermanifolds. A theorem is established that the structure sheaf of any DeWitt G-supermanifold is acyclic.

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Available abstract

In this present paper de Rham cohomology of graded manifolds, cohomology of graded differential forms and cohomology of DeWitt supermanifolds are studied. The structure of a G-supermanifold in general is not acyclic. So, the cohomology is defined via the complex of graded differential forms. This situation is investigated together with the graded Dolbeault cohomology of complex G-supermanifolds. A theorem is established that the structure sheaf of any DeWitt G-supermanifold is acyclic.

Key concepts: Supermanifold, Mathematics, Sheaf cohomology, De Rham cohomology, Cohomology, Sheaf, Pure mathematics, Exterior algebra

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