Comultiplicativity of the Ozsváth-szabó Contact Invariant
نویسنده
چکیده
Suppose that S is a surface with boundary and that g and h are diffeomorphisms of S which restrict to the identity on the boundary. Let Yg, Yh, and Yh◦g be the threemanifolds with open book decompositions given by (S, g), (S, h), and (S, h ◦ g), respectively. We show that the Ozsváth-Szabó contact invariant is natural under a comultiplication map μ̃ : d HF (−Yh◦g) → d HF (−Yg)⊗ d HF (−Yh). It follows that if the contact invariants associated to the open books (S, g) and (S, h) are non-zero then the contact invariant associated to the open book (S, h ◦ g) is also non-zero.
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