Absolutely Graded Floer homologies and intersection forms for four-manifolds with boundary

Details Absolutely Graded Floer homologies and intersection forms for four-manifolds with boundary Absolutely Graded Floer homologies and intersection forms for four-manifolds with boundary

2001-10-16

arxiv.org/abs/math/0110170v2

Mathematics

Symplectic Geometry

Corrected references in the lens space surgeries section. Also, strengthened the statement of lens space surgeries theorem (Th

Scientific paper

In an earlier paper (math.SG/0110169), we introduced absolute gradings on the three-manifold invariants developed in math.SG/0101206 and math.SG/0105202. Coupled with the surgery long exact sequences, we obtain a number of three- and four-dimensional applications of this absolute grading including strengthenings of the ``complexity bounds'' (from math.SG/0101206), restrictions on knots whose surgeries give rise to lens spaces, and calculations of $\HFp$ for a variety of three-manifolds. Moreover, we show how the structure of $\HFp$ constrains the exoticness of definite intersection forms for smooth four-manifolds which bound a given three-manifold. In addition to these new applications, the techniques also provide alternate proofs of Donaldson's diagonalizability theorem and the Thom conjecture for $\CP{2}$.

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