We explore the interplay between contact structures and sutured monopole Floer
homology. First, we study the behavior of contact elements, which were defined by
Baldwin and Sivek, under the operation of performing Floer excisions, which was
introduced to the context of sutured monopole Floer homology by Kronheimer and
Mrowka. We then compute the sutured monopole Floer homology of some special
balanced sutured manifolds, using tools closely related to contact geometry. For an
application, we obtain an exact triangle for the oriented skein relation in monopole
theory and derive a connected sum formula for sutured monopole Floer
homology.
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