On the algebra of cornered Floer homology
On the algebra of cornered Floer homology
复制标题
角Floer同调的代数
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Ciprian Manolescu
中科院分区：
文献类型：
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作者：
Christopher L. Douglas;Ciprian Manolescu
有界Floer同调将一个参数化定向曲面与一个微分分次代数联系起来。我们研究了该代数在曲面分裂下的性质。对于圆，我们关联一个微分分次2-代数，nil-Coxeter序列2-代数，并且对于具有连通边界的曲面，关联一个在这个2-代数上的代数模，使得满足自然胶合性质。此外，考虑到具有余维2角的三维流形的潜在Floer同调理论的结构，我们给出了平面网格图的Floer复形关于垂直和水平切片的分解定理。
Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2‐algebra, the nil‐Coxeter sequential 2‐algebra and to a surface with connected boundary an algebra‐module over this 2‐algebra, such that a natural gluing property is satisfied. Moreover, with a view towards the structure of a potential Floer homology theory of 3‐manifolds with codimension‐2 corners, we present a decomposition theorem for the Floer complex of a planar grid diagram, with respect to vertical and horizontal slicing.