1,359 research outputs found

    Acyclic curves and group actions on affine toric surfaces

    No full text

    Cyclic metric Lie groups

    Get PDF
    Cyclic metric Lie groups are Lie groups equipped with a left-invariant metric which is in some way far from being biinvariant, in a sense made explicit in terms of Tricerri and Vanhecke's homogeneous structures. The semisimple and solvable cases are studied. We extend to the general case, Kowalski-Tricerri's and Bieszk's classifications of connected and simply-connected unimodular cyclic metric Lie groups for dimensions less than or equal to five

    Three themes in the work of Charles Ehresmann: Local-to-global; Groupoids; Higher dimensions

    Full text link
    This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored.Comment: 13 pages; Expansion of an invited talk given to the 7th Conference on the Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann, Bedlewo 8.05.2005-15.05.2005 (Poland) Version 2: corrections of a date and some grammar, slight referencing changes, and a small comment added Version4. Theorem 2.2 got corrected and then uncorrected! It is now corrected. Version5. Reference added. Various minor improvements made in reaction to comment

    Isomorphism in expanding families of indistinguishable groups

    Full text link
    For every odd prime pp and every integer n≥12n\geq 12 there is a Heisenberg group of order p5n/4+O(1)p^{5n/4+O(1)} that has pn2/24+O(n)p^{n^2/24+O(n)} pairwise nonisomorphic quotients of order pnp^{n}. Yet, these quotients are virtually indistinguishable. They have isomorphic character tables, every conjugacy class of a non-central element has the same size, and every element has order at most pp. They are also directly and centrally indecomposable and of the same indecomposability type. The recognized portions of their automorphism groups are isomorphic, represented isomorphically on their abelianizations, and of small index in their full automorphism groups. Nevertheless, there is a polynomial-time algorithm to test for isomorphisms between these groups.Comment: 28 page
    • …
    corecore