“…How do index theorems extend to these spaces? [40] What is an appropriate mathematical supercohomology theory? How are singularities resolved for supermanifolds?…”
By providing a general correspondence between Landau-Ginzburg orbifolds and nonlinear sigma models, we find that the elusive mirror of a rigid manifold is actually a supermanifold. We also discuss when sigma models with super-target spaces are conformally invariant and describe their chiral rings. Both supermanifolds with and without Kähler moduli are considered. This work leads us to conclude that mirror symmetry should be viewed as a relation among super-varieties rather than bosonic varieties. 4/94 * Supported by the Fannie and John Hertz Foundation and the Beinecke Memorial Fellowship. † (sethi@string.harvard.edu)
“…How do index theorems extend to these spaces? [40] What is an appropriate mathematical supercohomology theory? How are singularities resolved for supermanifolds?…”
By providing a general correspondence between Landau-Ginzburg orbifolds and nonlinear sigma models, we find that the elusive mirror of a rigid manifold is actually a supermanifold. We also discuss when sigma models with super-target spaces are conformally invariant and describe their chiral rings. Both supermanifolds with and without Kähler moduli are considered. This work leads us to conclude that mirror symmetry should be viewed as a relation among super-varieties rather than bosonic varieties. 4/94 * Supported by the Fannie and John Hertz Foundation and the Beinecke Memorial Fellowship. † (sethi@string.harvard.edu)
Enantiomerically enriched epoxides are useful intermediates that have found many applications in asymmetric synthesis, and development of efficient catalysts for asymmetric epoxidation has received considerable attention. In this manuscript we describe the design, preparation, and use of new highly selective iminium salt organocatalysts for asymmetric
“…373 The oxidation of isoborneol (379) to camphor, using polymersupported CrO,, has been described. 374 Bornyl chloride (432) reacts with urea to give (433),375 and bornylmagnesium chloride reacts with benzaldehyde in THF solution to give bornene (434), benzyl alcohol, and a small amount of benzoin. 376 Camphor derivatives continue to be applied successfully as chiral auxiliaries for organic synthesis.…”
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