A geometric realization of silting theory for gentle algebras

A gentle algebra gives rise to a dissection of an oriented marked surface with boundary into polygons and the bounded derived category has geometric interpretation in terms this surface. In paper we study silting theory its underlying particular, show how mutation corresponds changing graded arcs that some cases results octahedral axioms flipping diagonals quadrilateral as work Dyckerhoff Kapranov (J Eur Math Soc 20(6):1473–1524, 2018) context triangulated surfaces. We also cutting along curve without self-intersections reduction. This is analogous Calabi–Yau reduction cluster categories shown by Marsh Palu (Proc Lond (3) 108(2):411–440, 2014) Qiu Zhou (Compos 153(9):1779–1819, 2017).