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How to caculate the internal hom of supermanifolds?
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Morphisms between supermanifolds R^{0|1}→R^{0|1}
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Are there oriented $4k+2$ manifolds such that $im(H_{2k+1}(M; Z/2)\to H_{2k+1}(M, \partial M; Z/2))$ has odd dimension?
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Equivariant Surgery problem
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Collapsing contractible subsets of the two-disk.
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Thematic Programs for 2010-2011?