منابع مشابه
Involutive Heegaard Floer Homology
Using the conjugation symmetry on Heegaard Floer complexes, we define a three-manifold invariant called involutive Heegaard Floer homology, which is meant to correspond to Z4-equivariant Seiberg-Witten Floer homology. Further, we obtain two new invariants of homology cobordism, d and d̄, and two invariants of smooth knot concordance, V 0 and V 0. We also develop a formula for the involutive Heeg...
متن کاملOn the Algebra of Cornered Floer Homology
Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2-algebra, the nilCoxeter sequential 2-algebra, and to a surface with connected boundary an algebra-module over this 2-algebra, such that a natural gluing property is...
متن کاملHeegaard diagrams and Floer homology
We review the construction of Heegaard–Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link complement, the slice genus of a knot, and the unknotting number of a knot. We emphasize the application to the Thurston norm, and illustrate the theory in the ...
متن کاملHeegaard Floer Homology and Alternating Knots
In [23] we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y , which is closely related to the Heegaard Floer homology of Y (c.f. [21]). In this paper we investigate some properties of these knot homology groups for knots in the three-sphere. We give a combinatorial description for the generators of the chain complex and their gradings. With the help of th...
متن کاملHeegaard Floer Homology of Mapping Tori Ii
We extend the techniques in a previous paper to calculate the Heegaard Floer homology groups HF(M, s) for fibered 3-manifolds M whose monodromy is a power of a Dehn twist about a genus-1 separating circle on a surface of genus g ≥ 2, where s is a non-torsion spinc structure on M .
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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2019
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/1266