کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6426003 | 1345409 | 2012 | 50 صفحه PDF | دانلود رایگان |
Lagrangian Floer homology in a general case has been constructed by Fukaya, Oh, Ohta and Ono, where they construct an Aâ-algebra or an Aâ-bimodule from Lagrangian submanifolds. They developed obstruction and deformation theories of the Lagrangian Floer homology theory. But for obstructed Lagrangian submanifolds, the standard Lagrangian Floer homology cannot be defined.We explore several well-known homology theories on these Aâ-objects, which are Hochschild and cyclic homology for an Aâ-objects and Chevalley-Eilenberg or cyclic Chevalley-Eilenberg homology for their underlying Lâ-objects. We show that these homology theories are well-defined and invariant even in the obstructed cases. Due to the existence of m0, the standard homological algebra does not work and we develop analogous homological algebra over Novikov fields.We provide computations of these homology theories in some cases: We show that for an obstructed Aâ-algebra with a non-trivial primary obstruction, Chevalley-Eilenberg Floer homology vanishes, whose proof is inspired by the comparison with cluster homology theory of Lagrangian submanifolds by Cornea and Lalonde.In contrast, we also provide an example of an obstructed case whose cyclic Floer homology is non-vanishing.
Journal: Advances in Mathematics - Volume 229, Issue 2, 30 January 2012, Pages 804-853