Elliptic cohomology Ell* is one of the so-called complex-oriented cohomology theories which generalizes the complex K-Theory and from which does not exist yet an strict geometric construction. Because the supercharge of the supersymmetric nonlinear sigma model plays a role similar to the role of the Dirac operator in K-theory, in this work we survey the string theory structure as one of the ingredients that would gives rise to a geometric construction for Ell*.
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