The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Saharon Shelah - One of the best experts on this subject based on the ideXlab platform.
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On Whitehead precovers
arXiv: Logic, 2017Co-Authors: Paul C. Eklof, Saharon ShelahAbstract:Author(s): Eklof, Paul C; Shelah, Saharon | Abstract: It is proved undecidable in ZFC + GCH whether every Z-module has a^{perp} {Z}-precover.
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Test Groups for Whitehead Groups
arXiv: Logic, 2007Co-Authors: Paul C. Eklof, László Fuchs, Saharon ShelahAbstract:We consider the question of when the dual of a Whitehead group is a test group for Whitehead groups. This turns out to be equivalent to the question of when the tensor product of two Whitehead groups is Whitehead. We investigate what happens in different models of set theory.
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Uniformization and the diversity of Whitehead groups
arXiv: Logic, 1992Co-Authors: Paul C. Eklof, Alan H. Mekler, Saharon ShelahAbstract:The connections between Whitehead groups and uniformization properties were investigated by the third author in [Sh:98]. In particular it was essentially shown there that there is a non-free Whitehead (respectively, aleph_1-coseparable) group of cardinality aleph_1 if and only if there is a ladder system on a stationary subset of omega_1 which satisfies 2-uniformization (respectively, omega-uniformization). These techniques allowed also the proof of various independence and consistency results about Whitehead groups, for example that it is consistent that there is a non-free Whitehead group of cardinality aleph_1 but no non-free aleph_1-coseparable group. However, some natural questions remained open, among them the following two: (i) Is it consistent that the class of W-groups of cardinality aleph_1 is exactly the class of strongly aleph_1-free groups of cardinality aleph_1 ? (ii) If every strongly aleph_1-free group of cardinality aleph_1 is a W-group, are they also all aleph_1-coseparable? In this paper we use the techniques of uniformization to answer the first question in the negative and give a partial affirmative answer to the second question.
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Uniformization and the diversity of Whitehead groups
Israel Journal of Mathematics, 1992Co-Authors: Paul C. Eklof, Alan H. Mekler, Saharon ShelahAbstract:Techniques of uniformization are used to prove that it is not consistent that the Whitehead groups of cardinality ℵ1 are exactly the strongly ℵ1-free groups. Some consequences of the assumption that every strongly ℵ1-free group of cardinality ℵ1 is Whitehead are derived. Other results about uniformization are also proved.
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On Whitehead modules
Journal of Algebra, 1991Co-Authors: Paul C. Eklof, Saharon ShelahAbstract:It is proved that it is consistent with ZFC + GCH that, for any reasonable ring R, for every R-module K there is a non-projective module M such that ExtR1(M, K) = 0; in particular, there are Whitehead R-modules which are not projective. This is generalized to show that it is consistent that, for certain rings R, there are Whitehead R-modules which are not the union of a continuous chain of submodules so that all quotients are small Whitehead R-modules. An application to Baer modules is also given: it is proved undecidable in ZFC + GCH whether there is a single test module for being a Baer module. © 1991.
Anh T. Tran - One of the best experts on this subject based on the ideXlab platform.
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The A-polynomial 2-tuple of twisted Whitehead links
International Journal of Mathematics, 2018Co-Authors: Anh T. TranAbstract:We compute the A-polynomial 2-tuple of twisted Whitehead links. As applications, we determine the canonical component of twisted Whitehead links and give a formula for the volume of twisted Whitehead link cone-manifolds.
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The A-polynomial 2-tuple of twisted Whitehead links
arXiv: Geometric Topology, 2016Co-Authors: Anh T. TranAbstract:We compute the A-polynomial 2-tuple of twisted Whitehead links. As applications, we determine canonical components of twisted Whitehead links and give a formula for the volume of twisted Whitehead link cone-manifolds.
Paul C. Eklof - One of the best experts on this subject based on the ideXlab platform.
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On Whitehead precovers
arXiv: Logic, 2017Co-Authors: Paul C. Eklof, Saharon ShelahAbstract:Author(s): Eklof, Paul C; Shelah, Saharon | Abstract: It is proved undecidable in ZFC + GCH whether every Z-module has a^{perp} {Z}-precover.
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Test Groups for Whitehead Groups
arXiv: Logic, 2007Co-Authors: Paul C. Eklof, László Fuchs, Saharon ShelahAbstract:We consider the question of when the dual of a Whitehead group is a test group for Whitehead groups. This turns out to be equivalent to the question of when the tensor product of two Whitehead groups is Whitehead. We investigate what happens in different models of set theory.
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Uniformization and the diversity of Whitehead groups
arXiv: Logic, 1992Co-Authors: Paul C. Eklof, Alan H. Mekler, Saharon ShelahAbstract:The connections between Whitehead groups and uniformization properties were investigated by the third author in [Sh:98]. In particular it was essentially shown there that there is a non-free Whitehead (respectively, aleph_1-coseparable) group of cardinality aleph_1 if and only if there is a ladder system on a stationary subset of omega_1 which satisfies 2-uniformization (respectively, omega-uniformization). These techniques allowed also the proof of various independence and consistency results about Whitehead groups, for example that it is consistent that there is a non-free Whitehead group of cardinality aleph_1 but no non-free aleph_1-coseparable group. However, some natural questions remained open, among them the following two: (i) Is it consistent that the class of W-groups of cardinality aleph_1 is exactly the class of strongly aleph_1-free groups of cardinality aleph_1 ? (ii) If every strongly aleph_1-free group of cardinality aleph_1 is a W-group, are they also all aleph_1-coseparable? In this paper we use the techniques of uniformization to answer the first question in the negative and give a partial affirmative answer to the second question.
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Uniformization and the diversity of Whitehead groups
Israel Journal of Mathematics, 1992Co-Authors: Paul C. Eklof, Alan H. Mekler, Saharon ShelahAbstract:Techniques of uniformization are used to prove that it is not consistent that the Whitehead groups of cardinality ℵ1 are exactly the strongly ℵ1-free groups. Some consequences of the assumption that every strongly ℵ1-free group of cardinality ℵ1 is Whitehead are derived. Other results about uniformization are also proved.
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On Whitehead modules
Journal of Algebra, 1991Co-Authors: Paul C. Eklof, Saharon ShelahAbstract:It is proved that it is consistent with ZFC + GCH that, for any reasonable ring R, for every R-module K there is a non-projective module M such that ExtR1(M, K) = 0; in particular, there are Whitehead R-modules which are not projective. This is generalized to show that it is consistent that, for certain rings R, there are Whitehead R-modules which are not the union of a continuous chain of submodules so that all quotients are small Whitehead R-modules. An application to Baer modules is also given: it is proved undecidable in ZFC + GCH whether there is a single test module for being a Baer module. © 1991.
Akira Yasuhara - One of the best experts on this subject based on the ideXlab platform.
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Whitehead DOUBLE AND MILNOR INVARIANTS
Osaka Journal of Mathematics, 2011Co-Authors: Jean-baptiste Meilhan, Akira YasuharaAbstract:We consider the operation of Whitehead double on a component of a link and study the behavior of Milnor invariants under this operation. We show that this operation turns a link whose Milnor invariants of length k are all zero into a link with vanishing Milnor invariants of length 2k 1, and we provide formulae for the first non-vanishing ones. As a consequence, we obtain sta tements relating the notions of link-homotopy and self -equivalence via the Whitehead double operation. By using our result, we show that a Brunnian link L is link-homotopic to the unlink if and only if the link L with a single component Whitehead doubled is self -equivalent to the unlink.
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Whitehead double and Milnor invariants
Osaka Journal of Mathematics, 2011Co-Authors: Jean-baptiste Meilhan, Akira YasuharaAbstract:We consider the operation of Whitehead double on a component of a link and study the behavior of Milnor invariants under this operation. We show that this operation turns a link whose Milnor invariants of length < k are all zero into a link with vanishing Milnor invariants of length < 2k, and we provide formulas for the first non-vanishing ones. As a consequence, we obtain statements relating the notions of link-homotopy and self Delta-equivalence via the Whitehead double operation. We show that a Brunnian link L is link-homotopic to the unlink if and only if a link L with a single component Whitehed doubled is self Delta-equivalent to the unlink.
Sergei V. Ivanov - One of the best experts on this subject based on the ideXlab platform.
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THE Whitehead ASPHERICITY CONJECTURE AND PERIODIC GROUPS
International Journal of Algebra and Computation, 1999Co-Authors: Sergei V. IvanovAbstract:The Whitehead asphericity conjecture claims that if is an aspherical group presentation, then for every the subpresentation is also aspherical. This conjecture is generalized for presentations of groups with periodic elements by introducing almost aspherical presentations (for example, every one-relator group is almost aspherical). It is proven that the generalized Whitehead asphericity conjecture (which claims that every subpresentation of an almost aspherical presentation is also almost aspherical) is equivalent to the original Whitehead conjecture. It is also proven that the generalized Whitehead asphericity conjecture holds for Ol'shanskii's presentations of free Burnside groups of large odd exponent, presentations of Tarski monsters and others.
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THE Whitehead ASPHERICITY CONJECTURE AND PERIODIC GROUPS
International Journal of Algebra and Computation, 1999Co-Authors: Sergei V. IvanovAbstract:The Whitehead asphericity conjecture claims that if [Formula: see text] is an aspherical group presentation, then for every [Formula: see text] the subpresentation [Formula: see text] is also aspherical. This conjecture is generalized for presentations of groups with periodic elements by introducing almost aspherical presentations (for example, every one-relator group is almost aspherical). It is proven that the generalized Whitehead asphericity conjecture (which claims that every subpresentation of an almost aspherical presentation is also almost aspherical) is equivalent to the original Whitehead conjecture. It is also proven that the generalized Whitehead asphericity conjecture holds for Ol'shanskii's presentations of free Burnside groups of large odd exponent, presentations of Tarski monsters and others.
