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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 375-389 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The cohomology theory of supermanifolds is developed. Its basic properties are established and simple examples given. The Wess-Zumino term in the Green-Schwarz covariant superstring action is interpreted as a nontrivial class in the “supersymmetric cohomology” of flat superspace. A quotient supermanifold with nontrivial topology reflecting this class is constructed. It is shown that there is no topological quantization condition for the coefficient of the Wess-Zumino term. The superstring differs from conventional sigma models in this respect because its action is Grassmann-valued and its group manifold (superspace) is noncompact.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 114 (1988), S. 131-145 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Super Riemann surfaces of genus 1, with arbitrary spin structures, are shown to be the sets of zeroes of certain polynomial equations in projective superspace. We conjecture that the same is true for arbitrary genus. Properties of superelliptic functions and super theta functions are discussed. The boundary of the genus 1 super moduli space is determined.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 137 (1991), S. 533-552 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A supersymmetric generalization of the Krichever map is used to construct algebro-geometric solutions to the various super Kadomtsev-Petviashvili (SKP) hierarchies. The geometric data required consist of a suitable algebraic supercurve of genusg (generallynot a super Riemann surface) with a distinguished point and local coordinates (z, θ) there, and a generic line bundle of degreeg−1 with a local trivialization near the point. The resulting solutions to the Manin-Radul SKP system describe coupled deformations of the line bundle and the supercurve itself, in contrast to the ordinary KP system which deforms line bundles but not curves. Two new SKP systems are introduced: an integrable “Jacobian” system whose solutions describe genuine Jacobian flows, deforming the bundle but not the curve; and a nonintegrable “maximal” system describing independent deformations of bundle and curve. The Kac-van de Leur SKP system describes the same deformations as the maximal system, but in a different parametrization.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 102 (1985), S. 123-137 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A DeWitt supermanifold always has the structure of a vector bundle over an ordinary spacetime manifold, whereas a Rogers supermanifold is not so restricted. Corresponding to the vector space fibers of the DeWitt supermanifold, a Rogers supermanifold has a foliation by submanifolds, or leaves, parametrized by soul coordinates only. We show that the universal covering space of any leaf always admits a flat metric. If the covering space is complete in this metric, it must in fact be a vector space. We combine this result with known theorems about foliations to give conditions under which a compact Rogers supermanifold with a single even dimension is necessarily a quotient space of flat superspace. We also show that a supermanifold defined by a polynomial equation in flat superspace is always of the DeWitt type. Finally, we exhibit new supermanifold structures forR 2 and the 2-torus which show that the foliation of a Rogers supermanifold can be quite exotic.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 100 (1985), S. 141-160 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct new examples of supermanifolds, and determine the vector bundle structure of the supermanifolds commonly used in physics. We show that any supermanifold admits a foliation whose leaves are locally tangent to the soul directions in the coordinate charts, and which is one of a nested sequence of foliations. We point out that the existence of these foliations implies restrictions on the possible topologies of supermanifolds. For example, a compact supermanifold with a single even dimension must have vanishing Euler characteristic. We also show that a globally defined superfield on a “nice” compact supermanifold must be constant along the leaves of the foliations. By this mechanism, the global topology of a supermanifold can be used to impose physically interesting constraints on superfields. As an example, we exhibit a supermanifold which has the local geometry of flat superspace but is such that all globally defined superfields are chiral.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 113 (1988), S. 601-623 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Teichmüller theory for super Riemann surfaces is rigorously developed using the supermanifold theory of Rogers. In the case of trivial topology in the soul directions, relevant for superstring applications, the following results are proven. The super Teichmüller space is a complex super-orbifold whose body is the ordinary Teichmüller space of the associated Riemann surfaces with spin structure. For genusg〉1 it has 3g-3 complex even and 2g-2 complex odd dimensions. The super modular group which reduces super Teichmüller space to super moduli space is the ordinary modular group; there are no new discrete modular transformations in the odd directions. The boundary of super Teichmüller space contains not only super Riemann surfaces with pinched bodies, but Rogers supermanifolds having nontrivial topology in the odd dimensions as well. We also prove the uniformization theorem for super Riemann surfaces and discuss their representation by discrete supergroups of Fuchsian and Schottky type and by Beltrami differentials. Finally we present partial results for the more difficult problem of classifying super Riemann surfaces of arbitrary topology.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 103 (1986), S. 431-439 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Recent results on the global structure of supermanifolds are used to define a notion of Berezin integration on any purely fermionic Rogers supermanifold. This leads to an integration theory on a large class of supermanifolds having both bosonic and fermionic coordinates. The existence of global functions and forms on such supermanifolds is discussed, as is some elementary cohomology of supermanifolds.
    Type of Medium: Electronic Resource
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