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edit approved Jul 3, 2017 at 0:04
Ali Taghavi
edit approved Jul 3, 2017 at 0:04
Ali Taghavi
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j.c.
j.c.
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In 1994, Mike Hopkins wrote a paper called Topological Modular Forms, the Witten Genus, and the Theorem of the CubeTopological Modular Forms, the Witten Genus, and the Theorem of the Cube. As usual, the introduction was fantastic, explaining the power of various cobordism invariants and connections between homotopy theory and other fields. He states "it is believed that there is an "index" theorem relating analysis on loop space to elliptic cohomology. So far, a satisfying mathematical theory is lacking."

What is the status of this question? Has such a theory been developed?

In 1994, Mike Hopkins wrote a paper called Topological Modular Forms, the Witten Genus, and the Theorem of the Cube. As usual, the introduction was fantastic, explaining the power of various cobordism invariants and connections between homotopy theory and other fields. He states "it is believed that there is an "index" theorem relating analysis on loop space to elliptic cohomology. So far, a satisfying mathematical theory is lacking."

What is the status of this question? Has such a theory been developed?

In 1994, Mike Hopkins wrote a paper called Topological Modular Forms, the Witten Genus, and the Theorem of the Cube. As usual, the introduction was fantastic, explaining the power of various cobordism invariants and connections between homotopy theory and other fields. He states "it is believed that there is an "index" theorem relating analysis on loop space to elliptic cohomology. So far, a satisfying mathematical theory is lacking."

What is the status of this question? Has such a theory been developed?

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David White
David White
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Atiyah-Singer style index theorem for elliptic cohomology?

In 1994, Mike Hopkins wrote a paper called Topological Modular Forms, the Witten Genus, and the Theorem of the Cube. As usual, the introduction was fantastic, explaining the power of various cobordism invariants and connections between homotopy theory and other fields. He states "it is believed that there is an "index" theorem relating analysis on loop space to elliptic cohomology. So far, a satisfying mathematical theory is lacking."

What is the status of this question? Has such a theory been developed?