# Contact monoids and Stein cobordisms - Mathematics > Symplectic Geometry

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Abstract: Suppose S is a compact surface with boundary, and let g be a diffeomorphismof S which fixes the boundary pointwise. We denote by M {S,g},\xi {S,g}\$ thecontact 3-manifold compatible with the open book S,g. In this article, weconstruct a Stein cobordism from the contact connected sum M {S,h},\xi {S,h}# M {S,g},\xi {S,g} to M {S,hg},\xi {S,hg}, for any two boundary-fixingdiffeomorphisms h and g. This cobordism accounts for the comultiplication mapon Heegaard Floer homology discovered in an earlier paper by the author, and itilluminates several geometrically interesting monoids in the mapping classgroup of S. We derive some consequences for the fillability of contactmanifolds obtained as cyclic branched covers of transverse knots.

Autor: John A. Baldwin

Fuente: https://arxiv.org/