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A gentle algebra gives rise to a dissection of an oriented marked surfacewith boundary into polygons and the bounded derived category of the gentlealgebra has a geometric interpretation in terms of this surface. In this paperwe study silting theory in the bounded derived category of a gentle algebra interms of its underlying surface. In particular, we show how silting mutationcorresponds to the changing of graded arcs and that in some cases siltingmutation results in the interpretation of the octahedral axioms in terms of theflipping of diagonals in a quadrilateral as in the work of Dyckerhoff-Kapranovin the context of triangulated surfaces. We also show that silting reductioncorresponds to the cutting of the underlying surface as is the case forCalabi-Yau reduction of surface cluster categories as shown by Marsh-Palu andQiu-Zhou.

A geometric realization of silting theory for gentle algebras