Frobenius∞ invariants of homotopy Gerstenhaber algebras, I
Frobenius∞ invariants of homotopy Gerstenhaber algebras, I
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同伦 Gerstenhaber 代数的 Frobenius∞ 不变量，I
DOI：
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发表时间：
2000
期刊：
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通讯作者：
S. Merkulov
中科院分区：
文献类型：
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作者：
S. Merkulov
我们从有限维上同调的同伦Gerstenhaber代数的派生范畴g到所谓的纯几何范畴F∞-流形构造了一个函子。后者包含作为子范畴的Frobenius流形(这样，一个指向的Frobenius流形本身就是同伦Gertenhaber代数)。如果g恰好是形式的L∞-代数，则它的F-∞-流形具有Gauss-Manin联系。讨论了镜像对称性的含义。
We construct a functor from the derived category of homotopy Gerstenhaber algebras, g, with finite-dimensional cohomology to the purely geometric category of so-called F∞-manifolds. The latter contains Frobenius manifolds as a subcategory (so that a pointed Frobenius manifold is itself a homotopy Gerstenhaber algebra). If g happens to be formal as a L∞-algebra, then its F∞-manifold comes equipped with the Gauss-Manin connection. Mirror Symmetry implications are discussed.