Constructing and Forbidding Automorphisms in Lifted Maps
نویسندگان
چکیده
We use an algebraic description of surfaces with boundary to study covering maps. The focus is on the relationship between automor-phisms in the base and lifted maps. We show how to introduce and/or prohibit additional automorphisms in the lift. Using this control we give proofs of MacBeath's Theorem, Gr unbaum's Conjecture, and settle a conjecture of Nedela and Skoviera.
منابع مشابه
Regular Homomorphisms and Regular Maps
Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms. This kind of map homomorphism is studied in detail, and generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving. Reconstruction is treated by means of voltage assignments on angles, a natural extension of the common assignments on darts. ...
متن کاملPetrie-Coxeter Maps Revisited
This paper presents a technique for constructing new chiral or regular polyhedra (or maps) from self-dual abstract chiral polytopes of rank 4. From improperly self-dual chiral polytopes we derive “Petrie-Coxeter-type” polyhedra (abstract chiral analogues of the classical Petrie-Coxeter polyhedra) and investigate their groups of automorphisms.
متن کاملEvaluating the Potential Area for Constructing Photovoltaic Power Plant in Iran using Fuzzy Approach
Solar energy is an important source of renewable, sustainable, and accessible kind of energy in the world. Halting environmental degradation, this kind of energy is what can reduce the damaging consequences of fossil fuels. Iran or other counties located in the arid area can use this type of energy. In fact, the geographical position of Iran in word's dry belt makes this country a proper land ...
متن کاملNew Approaches in Black Box Group Theory
We introduce a new approach in black box group theory which deals with black box group problems in the category of black boxes and their morphisms. This enables us to enrich black box groups by actions of outer automorphisms such as Frobenius maps or graph automorphisms of simple groups of Lie type. As an application of this new technique, we present a number of new results, including a solutio...
متن کاملDesigns over the binary field from the complete monomial group
All known direct constructions of designs over finite fields arise by subgroups of the normalizer of a Singer cycle, by lifted special linear groups, or lifted general linear groups. Other types of non-trivial automorphism groups for which designs over finite fields do exist have not been mentioned so far. In this paper we construct the first non-trivial designs over finite fields admitting the...
متن کامل