Abstract
In this paper, we propose so-called fattened complex
manifolds as target spaces for the topological B-model. We naturally
obtain these manifolds by restricting the structure sheaf of the
= 4 supertwistor space, a process, which can be
understood as a fermionic dimensional reduction. Using the
twistorial description of these fattened complex manifolds, we
construct Penrose-Ward transforms between solutions to the
holomorphic Chern-Simons equations on these spaces and bosonic
subsectors of solutions to the = 4 self-dual Yang-Mills
equations on 
4or 
4. Furthermore, we
comment on Yau's theorem for these spaces.
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