The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform

Koen Struyve - One of the best experts on this subject based on the ideXlab platform.

Makoto Sakuma - One of the best experts on this subject based on the ideXlab platform.

  • Epimorphisms from 2-bridge link groups onto Heckoid groups (II)
    arXiv: Geometric Topology, 2012
    Co-Authors: Donghi Lee, Makoto Sakuma
    Abstract:

    In Part I of this series of papers, we made Riley's definition of Heckoid groups for 2-bridge links explicit, and gave a systematic construction of Epimorphisms from 2-bridge link groups onto Heckoid groups, generalizing Riley's construction. In this paper, we give a complete characterization of upper-meridian-pair-preserving Epimorphisms from 2-bridge link groups onto even Heckoid groups, by proving that they are exactly the Epimorphisms obtained by the systematic construction.

  • Epimorphisms between 2-bridge link groups
    The Zieschang Gedenkschrift, 2008
    Co-Authors: Tomotada Ohtsuki, Robert Riley, Makoto Sakuma
    Abstract:

    We give a systematic construction of Epimorphisms between 2‐bridge link groups. Moreover, we show that 2‐bridge links having such an Epimorphism between their link groups are related by a map between the ambient spaces which only have a certain specific kind of singularity. We show applications of these Epimorphisms to the character varieties for 2‐bridge links and 1 ‐dominating maps among 3‐ manifolds.

Jorge Vitória - One of the best experts on this subject based on the ideXlab platform.

  • Flat ring Epimorphisms and universal localizations of commutative rings
    The Quarterly Journal of Mathematics, 2020
    Co-Authors: Lidia Angeleri Hügel, Frederik Marks, Jan Stovicek, Ryo Takahashi, Jorge Vitória
    Abstract:

    Abstract We study different types of localizations of a commutative noetherian ring. More precisely, we provide criteria to decide: (a) if a given flat ring Epimorphism is a universal localization in the sense of Cohn and Schofield; and (b) when such universal localizations are classical rings of fractions. In order to find such criteria, we use the theory of support and we analyse the specialization closed subset associated to a flat ring Epimorphism. In case the underlying ring is locally factorial or of Krull dimension one, we show that all flat ring Epimorphisms are universal localizations. Moreover, it turns out that an answer to the question of when universal localizations are classical depends on the structure of the Picard group. We furthermore discuss the case of normal rings, for which the divisor class group plays an essential role to decide if a given flat ring Epimorphism is a universal localization. Finally, we explore several (counter)examples which highlight the necessity of our assumptions.

  • Silting modules and ring Epimorphisms
    Advances in Mathematics, 2016
    Co-Authors: Lidia Angeleri Hügel, Frederik Marks, Jorge Vitória
    Abstract:

    Abstract There are well-known constructions relating ring Epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring Epimorphism which we describe explicitly as an idempotent quotient of the endomorphism ring of the Bongartz completion. For hereditary rings, this assignment is used to parametrise homological ring Epimorphisms by silting modules. We further show that homological ring Epimorphisms of a hereditary ring form a lattice which completes the poset of noncrossing partitions in the case of finite dimensional algebras.

  • From ring Epimorphisms to universal localisations
    arXiv: Rings and Algebras, 2012
    Co-Authors: Frederik Marks, Jorge Vitória
    Abstract:

    For a fixed ring, different classes of ring Epimorphisms and localisation maps are compared. In fact, we provide sufficient conditions for a ring Epimorphism to be a universal localisation. Furthermore, we consider recollements induced by some homological ring Epimorphisms and investigate whether they yield recollements of derived module categories.

Lidia Angeleri Hügel - One of the best experts on this subject based on the ideXlab platform.

  • Flat ring Epimorphisms and universal localizations of commutative rings
    The Quarterly Journal of Mathematics, 2020
    Co-Authors: Lidia Angeleri Hügel, Frederik Marks, Jan Stovicek, Ryo Takahashi, Jorge Vitória
    Abstract:

    Abstract We study different types of localizations of a commutative noetherian ring. More precisely, we provide criteria to decide: (a) if a given flat ring Epimorphism is a universal localization in the sense of Cohn and Schofield; and (b) when such universal localizations are classical rings of fractions. In order to find such criteria, we use the theory of support and we analyse the specialization closed subset associated to a flat ring Epimorphism. In case the underlying ring is locally factorial or of Krull dimension one, we show that all flat ring Epimorphisms are universal localizations. Moreover, it turns out that an answer to the question of when universal localizations are classical depends on the structure of the Picard group. We furthermore discuss the case of normal rings, for which the divisor class group plays an essential role to decide if a given flat ring Epimorphism is a universal localization. Finally, we explore several (counter)examples which highlight the necessity of our assumptions.

  • Silting modules and ring Epimorphisms
    Advances in Mathematics, 2016
    Co-Authors: Lidia Angeleri Hügel, Frederik Marks, Jorge Vitória
    Abstract:

    Abstract There are well-known constructions relating ring Epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring Epimorphism which we describe explicitly as an idempotent quotient of the endomorphism ring of the Bongartz completion. For hereditary rings, this assignment is used to parametrise homological ring Epimorphisms by silting modules. We further show that homological ring Epimorphisms of a hereditary ring form a lattice which completes the poset of noncrossing partitions in the case of finite dimensional algebras.

Masaaki Suzuki - One of the best experts on this subject based on the ideXlab platform.

  • Generating function on Epimorphisms between $2$-bridge knot groups
    arXiv: Geometric Topology, 2020
    Co-Authors: Masaaki Suzuki
    Abstract:

    We have the generating function which determines the number of $2$-bridge knot groups admitting Epimorphisms onto the knot group of a given $2$-bridge knot, in terms of crossing number. In this paper, we will refine this formula by taking account into genus as well as crossing number. Next, we determine the number of Epimorphisms between fibered $2$-bridge knot groups. Moreover, we discuss degree one maps and $2$-bridge knots uknotting number one.

  • Non-meridional Epimorphisms of knot groups
    Algebraic & Geometric Topology, 2016
    Co-Authors: Jae Choon Cha, Masaaki Suzuki
    Abstract:

    In the literature of the study of knot group Epimorphisms, the existence of an Epimorphism between two given knot groups is mostly (if not always) shown by giving an Epimorphism which preserves meridians. A natural question arises: is there an Epimorphism preserving meridians whenever a knot group is a homomorphic image of another? We answer in the negative by presenting infinitely many pairs of prime knot groups (G,G') such that G' is a homomorphic image of G but no Epimorphism of G onto G' preserves meridians.