Ghost number 2

Ghost number 2 should correspond to the physical vertex operators:

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We have only studied them in flat space.

As we will explain, there is a puzzle even in flat space.

It is more convenient to study the homology , instead of the cohomology. The relation between them is the Poincare duality:

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The homology has a very straightforward elementary description. It consists of the elements of the form:

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