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Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology

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Şavk,  Oğuz
Max Planck Institute for Mathematics, Max Planck Society;

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Karakurt, Ç., & Şavk, O. (2022). Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology. Acta Mathematica Hungarica, 168(2), 454-489. doi:10.1007/s10474-022-01280-9.


Cite as: https://hdl.handle.net/21.11116/0000-000C-0238-3
Abstract
Continuing our previous work in [23], we effectively compute connected Heegaard Floer homologies of two families of Brieskorn spheres realized as the boundaries of almost simple linear graphs. Using Floer theoretic invariants of Dai, Hom, Stoffregen, and Truong [6], we show that these Brieskorn spheres also generate infinite rank summands in the homology cobordism group. Our computations also have applications to the concordance of classical knots and 0-concordance of 2-knots.