Now showing items 1-20 of 26

  • An A(infinity)Operad in Spineless Cacti 

    Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew (2015-11-01)
    Article
    Open Access
    The dg operad of cellular chains on the operad of spineless cacti of Kaufmann (Topology 46(1):39-88, 2007) is isomorphic to the Gerstenhaber-Voronov dg operad codifying the cup product and brace operations on the Hochschild ...
  • André spectral sequences for Baues-Wirsching cohomology of categories 

    Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew (2011-12-16)
    Other
    Open Access
    We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications ...
  • André spectral sequences for Baues–Wirsching cohomology of categories 

    Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew (2012-04-30)
    Article
    Restricted access - publisher's policy
    We construct spectral sequences in the framework of Baues–Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications ...
  • Decomposition spaces and restriction species 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (Oxford University Press, 2018-09-12)
    Article
    Restricted access - publisher's policy
    We show that Schmitt’s restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2-Segal spaces), and that their associated coalgebras are an instance of the general ...
  • Decomposition spaces, incidence algebras and Möbius inversion 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2014-04-11)
    External research report
    Open Access
  • Decomposition spaces, incidence algebras and Möbius inversion I: basic theory 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2015-12)
    External research report
    Open Access
    This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Möbius inversion, where algebraic identities are realised by taking homotopy cardinality ...
  • Decomposition spaces, incidence algebras and Möbius inversion I: basic theory 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2018-06-20)
    Article
    Restricted access - publisher's policy
    This is the first in a series of papers devoted to the theory of decomposition spaces, a general framework for incidence algebras and Möbius inversion, where algebraic identities are realised by taking homotopy cardinality ...
  • Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2015-12)
    External research report
    Open Access
    This is part 2 of a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition space ...
  • Decomposition spaces, incidence algebras and Mobius inversion II: Completeness, length filtration, and finiteness 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2018-07-31)
    Article
    Restricted access - publisher's policy
    This is the second in a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and Möbius inversion, with coefficients in 8-groupoids. A decomposition ...
  • Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2015-12)
    External research report
    Open Access
    Decomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors between decomposition spaces induce coalgebra ...
  • Decomposition spaces, incidence algebras and Mobius inversion III: the decomposition space of Möbius intervals 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2018-08-20)
    Article
    Restricted access - publisher's policy
    Decomposition spaces are simplicial 8-groupoids subject to a certain exactness condition, needed to induce a coalgebra structure on the space of arrows. Conservative ULF functors (CULF) between decomposition spaces induce ...
  • Decomposition spaces in combinatorics 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2016-12)
    External research report
    Open Access
    A decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new ...
  • Differential operators and the Witten genus for projective spaces and Milnor manifolds 

    Gálvez Carrillo, Maria Immaculada; Tonks, Andrew (2003)
    Article
    Open Access
    A $genus$ (in the sense of Hirzebruch [4]) is a multiplicative invariant of cobordism classes of manifolds. Classical examples include the numerical invariants given by the signature and the $\widehat{A}$- and Todd genera. ...
  • Estructuras A-infinito en la opérada de cactus 

    Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew (2012)
    Conference lecture
    Restricted access - publisher's policy
    Diversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una ...
  • Groupoids and Faà di Bruno formulae for Green functions in bialgebras of trees 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2014)
    Article
    Restricted access - publisher's policy
    We prove a Faà di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids.
  • Groupoids and Faà di Bruno Formulae for green functions in bialgebras of trees 

    Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Kock, Joachim (2012-07)
    External research report
    Open Access
    We prove a Faa di Bruno formula for the Green function in the bialgebra of P-trees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. For suitable choices ...
  • Homotopy Batalin-Vilkovisky Algebras 

    Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Vallette, Bruno (2012)
    Article
    Open Access
    This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define ...
  • Homotopy Batalin-Vilkovisky algebras 

    Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Vallette, Bruno (2011-03-30)
    Other
    Open Access
    This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define ...
  • Homotopy Gerstenhaber structures and vertex algebras 

    Gálvez Carrillo, Maria Immaculada; Gorbounov, V.; Tonks, Andrew (2010)
    Article
    Open Access
    We provide a simple construction of a G∞-algebra structure on an important class of vertex algebras V, which lifts the Gerstenhaber algebra structure on BRST cohomology of V introduced by Lian and Zuckerman. We outline two ...
  • Homotopy linear algebra 

    Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2016-02)
    External research report
    Open Access
    By homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices ...