Stable Complex Manifolds
نویسنده
چکیده
1. T. Van de Ven [3] has recently shown that there exist real 4dimensional manifolds which admit almost complex structures but admit no complex structures, e.g. SXS* # SXS # CP(2). The purpose of this note is to show that this is an unstable phenomenon. Let M be a C w-dimensional real manifold without boundary and let TM be its tangent bundle. R is real Euclidean fe-space and C is complex &-space. DEFINITION 1. M admits a stable complex structure if MXR can be given the structure of a complex analytic manifold for some k ^ 0, n = k (mod 2). Let £ be an m-plane bundle over M. DEFINITION 2. A stable complex structure for £ is a reduction of the group of (•»©€* to U((m+k)/2) for some feâO, m^k (mod 2). DEFINITION 3. A stable almost complex structure for M is a stable complex structure for TM>
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