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

Abstract

Continuing our previous work, 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, 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.

arXiv comment29 pages, 9 figures

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Cited by in corpus (4)

• A survey of the homology cobordism group
• Cables of the figure-eight knot via real Frøyshov invariants
• On homology planes and contractible $4$-manifolds
• Classical and new plumbed homology spheres bounding contractible manifolds and homology balls