Heegaard Floer Homology and Degree-One-Maps Between 3-Manifolds

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Bagherifard, Narges | 2021

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Type of Document: Ph.D. Dissertation
Language: Farsi
Document No: 54853 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fanai, Hamid Reza; Eftekhary, Eaman
Abstract:
Suppose that K and K^' are knots inside the homology spheres Y and Y^', respectively. Let X=Y(K,K^') be the 3-manifold obtained by splicing the complements of K and K^' and Z be the three-manifold obtained by 0-surgery on K. When Y^' is an L-space, we use Eftekhary's splicing formula to show that the rank of (HF) ̂(X) is bounded below by the rank of (HF) ̂(Y) if τ_(K^' )=0 and is bounded below by rank((HF) ̂(Z))-2 rank((HF) ̂(Y))+1 if τ_(K^' )≠0.
Keywords:
Three Dimentional Manifold ; Heegaard-Floer Homology ; Degree-One Maps ; Splicing Knot Complements ; Knot Floar Homology

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