Bordered Manifolds with Torus Boundary and the Link Surgery Formula

von Ian Zemke

Hardcover

Kurzbeschreibung des Verlags

In this memoir, we develop a theory of bordered \mathrm{HF}^- using the link surgery formula of Manolescu and Osváth. We interpret their link surgery complexes as type-\mathrm{D} modules over an associative algebra \mathcal{K}, which we introduce. We prove a connected sum formula, which we interpret as an A_\infty-tensor product over our algebra \mathcal{K}. Topologically, this connected sum formula may be viewed as a formula for gluing along torus boundary components.

We discuss several important examples. As a basic example, if K_1 and K_2 are knots in S^3, and Y is obtained by gluing the complements of K_1 and K_2 together using an orientation reversing diffeomorphism of their boundaries, then our theory may be used to compute \mathrm{CF}^-(Y) from \mathrm{CFK}^\infty(K_1) and \mathrm{CFK}^\infty(K_2). By computing the type-\mathrm{D} modules for rationally framed solid tori, our theory gives a version of the link surgery formula for rationally framed links. As a final example, we use our theory to derive the Heegaard Floer homology of all 3-manifolds which bound the plumbing of a tree of disk bundles over 2-spheres.

• Reihe: Memoirs of the European Mathematical Society
• Themen: Mathematik und Naturwissenschaften Mathematik Topologie
• ISBN: 9783985471102
• Sprache: Englisch
• Erscheinungsdatum: 01.07.2026
• Größe: 24 x 17 cm
• Verlag: EMS Press