Browsing by Author "Tonks, Andrew"

An A(infinity)Operad in Spineless Cacti
Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew (20151101)
Article
Open AccessThe dg operad of cellular chains on the operad of spineless cacti of Kaufmann (Topology 46(1):3988, 2007) is isomorphic to the GerstenhaberVoronov dg operad codifying the cup product and brace operations on the Hochschild ... 
André spectral sequences for BauesWirsching cohomology of categories
Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew (20111216)
Other
Open AccessWe construct spectral sequences in the framework of BauesWirsching 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 (20120430)
Article
Restricted access  publisher's policyWe 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, 20180912)
Article
Open AccessWe show that Schmitt’s restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2Segal 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 (20140411)
External research report
Open Access 
Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (201512)
External research report
Open AccessThis 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 (20180620)
Article
Restricted access  publisher's policyThis 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 (201512)
External research report
Open AccessThis 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 8groupoids. A decomposition space ... 
Decomposition spaces, incidence algebras and Mobius inversion II: Completeness, length filtration, and finiteness
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (20180731)
Article
Restricted access  publisher's policyThis 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 8groupoids. A decomposition ... 
Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (201512)
External research report
Open AccessDecomposition spaces are simplicial 8groupoids 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 (20180820)
Article
Restricted access  publisher's policyDecomposition spaces are simplicial 8groupoids 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 (201612)
External research report
Open AccessA decomposition space (also called unital 2Segal 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 AccessA $genus$ (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 Ainfinito en la opérada de cactus
Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew (2012)
Conference lecture
Restricted access  publisher's policyDiversas 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 policyWe prove a Faà di Bruno formula for the Green function in the bialgebra of Ptrees, 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 (201207)
External research report
Open AccessWe prove a Faa di Bruno formula for the Green function in the bialgebra of Ptrees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. For suitable choices ... 
Homotopy BatalinVilkovisky Algebras
Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Vallette, Bruno (2012)
Article
Open AccessThis paper provides an explicit cofibrant resolution of the operad encoding BatalinVilkovisky algebras. Thus it defines the notion of homotopy BatalinVilkovisky algebras with the required homotopy properties. To define ... 
Homotopy BatalinVilkovisky algebras
Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Vallette, Bruno (20110330)
Other
Open AccessThis paper provides an explicit cofibrant resolution of the operad encoding BatalinVilkovisky algebras. Thus it defines the notion of homotopy BatalinVilkovisky 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 AccessWe 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 (201602)
External research report
Open AccessBy homotopy linear algebra we mean the study of linear functors between slices of the 8category of 8groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices ...