We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

In this paper we study the reflexive subobject lattices and reflexive endomorphism algebras in a concrete category. For the category Set of sets and mappings, a complete characterization for both reflexive subobject lattices and reflexive endomorphism algebras is obtained. Some partial results are also proved for the category of abelian groups.

For a complex abelian surface A with endomorphism ring isomorphic to the maximal order in a quartic CM-field K, the Igusa invariants j1(A), j2(A), j3(A) generate an unramified abelian extension of the reflex field of K. In this paper we give an explicit geometric description of the Galois action of the class group of this reflex field on j1(A), j2(A), j3(A). Our description can be expressed by ...

It is proved that the periodic point submonoid of a free inverse monoid endomorphism is always finitely generated. Using Chomsky’s hierarchy of languages, we prove that the fixed point submonoid of an endomorphism of a free inverse monoid can be represented by a context-sensitive language but, in general, it cannot be represented by a context-free language.

An endomorphism φ of a free group is called primitivity preserving if φ takes every primitive element to another primitive. In this paper we prove that every primitivity preserving endomorphism of a free group of a finite rank n ≥ 3 is an automorphism.