Heegaard Floer Homology<br/>

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Heegaard Floer Homology

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41332 (02)
University: Sharif University of Technology
Department: Mathematical
Advisor(s): ahraini, Alireza
Abstract:
The main scope of this article is to identify Floer homology invariantsby means of Heegaard splitting of a 3-dimensional orientable manifoldY . Here by ” Heegaard splitting ” for Y , we mean decomposition Y =U ? U , where U and U are two balls with orientable g?handles,? ? ? ? ?gwich attached together on a closed oriented surface ? of boundary.gOne can identify this splitting by specifying two sets of oriented closedcurves ? = (? , ? , · · · , ? ) and ? = (? , ? , · · · , ? ) which live on ? .1 2 g 1 2 g gDesired invariants will be obtained by investigating g?order symmetricproducts of ? , denoted by SPg(? ) . in factT = ? × · · · × ? andg g ? 1 gT = ? × · · · × ? will play the role of Lagrangian submanifold in the? 1 gFloer homology of SPg(? ) , and by means of this complex manifoldgand its two totally real submanifolds T , T , for any SpinC structure? ? ds, Floer homology groups HF?(Y, s)? HF?(Y, s)? HF+(Y, s)? HF(Y, s) will be attributed to the manifold Y
Keywords:
Floer Homology ; Spin C Structure ; Symmetric Product ; Heegaard Diagram