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Mathoverflow.net news digest

  • 0 days

    Looking for bibliographic information about an apparently unpublished paper of B...

    I am trying to clarify the history/status of the following unpublished-looking manuscript:
    R. D. Byrd, J. T. Lloyd, F. D. Pedersen, and J. W. Stepp, Automorphisms of the semigroup of finite complexes of a torsion-free abelian group.
    The work is cited as "submitted" in a few papers from the late 1970s and early 1980s related to semigroups of complexes (now more commonly called power semigroups), for instance in:...

  • 2 months

    Universal cover of a semisimple algebraic group as a functor

    Let $k$ be a field of arbitrary characteristic, andlet $G$ be a (connected) semisimple group over $k$.Let $\widetilde G$ denote the universal cover of $G$.
    Question. What mathematical texts contain the following assertion: the assignment on objects$G \rightsquigarrow \widetilde G$extends to a functor from the category of semisimple $k$-groupsto the category of simply connected semisimple $k$-groups?...

  • 0 days

    Condensing the internal complex that subdivides a simplex

    Given a subdivided simplex A. What is a necessary and sufficient condition on the subdivision that will allow me to get another isomorphic subdivision with all the internalvertices living in as small neighborhood as I wish?
    DeepSeek says that the condition is that the complex remaining after removing the boundary of the simplex is collapsible. Given I know what is collapsible, but no Homotopy, PL, etc., is there any laywoman's explanation why it's true (if it's true)?...

  • 0 days

    Push-pull for Segre classes of coherent sheaves

    Let $\mathcal{F}$ be a coherent sheaf on a normal (but not necessarily smooth) projective variety $X$. Following Fulton's Intersection Theory, we can define its Segre class as$$ s(\mathcal{F}) =\sum_{i\geq 0} \pi_*(c_1(O(1))^i\cap \mathrm{Proj}(\mathrm...

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