Appears in collection : 2023 - T2 - WS1 - GAP XVIII: Homotopy algebras and higher structures

Euler continuants are universal polynomials expressing the numerator and denominator of a finite continued fraction whose entries are independent variable. Remarkably, they allow categorical lifts which are certain complexes constructed out of a functor and its iterated adjoints. The totalizations of these complexes can be seen as higher analogs of spherical twists and cotwists and lead to a generalization of spherical functors which we call N-spherical. They describe periodic semi-orthogonal decompositions (SODs) of triangulated (or, rather stable infinity-) categories. In fact, forming iterated mutations of an SOD can be seen as a categorical lift of forming a continued fraction. Joint work with T. Dyckerhoff, V. Schechtman.