On the algebra of operators corresponding to the union of smooth submanifolds (Q2083454)

Consider two transversally intersecting submanifolds in a smooth closed manifold. In this article, the authors give an algebraic description of all types of operators generated by pseudodifferential operators, boundary operators and coboundary operators corresponding to submanifolds. Following [\textit{B. Yu. Sternin}, Sov. Math., Dokl. 8, 41--45 (1967; Zbl 0177.37103); translation from Dokl. Akad. Nauk SSSR 172, 44--47 (1967)] a general element of this operator algebra is called a morphism. Generators of these morphisms are completely classified into 18 types. The notion of symbol of a morphism is introduced and the formula for the composition of two morphisms is derived as well. However, the study of ellipticity of morphisms is postponed to a sequel of this article.