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Cohomology of algebras over weak Hopf algebras

J. N. Alonso Álvarez, J. M. Fernández Vilaboa, R. González Rodríguez. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 341--369.Abstract: In this paper we present the Sweedler...

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A purely homotopy-theoretci proof of the Blakers-Massey theorem for $n$-cubes

Brian A. Munson. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 333--339.Abstract: Goodwillie’s proof of the Blakers-Massey Theorem for n- cubes relies on a lemma whose proof invokes...

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Global orthogonal spectra

Anna Marie Bohmann. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 313--332.Abstract: For any compact Lie group $G$, there are several well-established definitions of a...

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Graphs associated with simplicial complexes

A. Grigor'yan, Yu. V. Muranov, Shing-Tung Yau. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 295--311.Abstract: The cohomology of digraphs was introduced for the first time by...

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Mayer-Vietoris sequences in stable derivators

Moritz Groth, Kate Ponto, Michael Shulman. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 265--294.Abstract: We show that stable derivators, like stable model cate- gories, admit...

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Describing high-order statistical dependence using "concurrence topology,"...

Steven P. Ellis, Arno Klein. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 245--264.Abstract: In multivariate data analysis dependence beyond pair-wise can be important. With many...

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On connective $K$-theory of elementary abelian 2-groups and local duality

Geoffrey M. L. Powell. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 215--243.Abstract: The connective $ku$-(co)homology of elementary abelian $2$-groups is determined as a functor...

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Exact sequences of commutative monoids and semimodules

Jawad Y. Abuhlail. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 199--214.Abstract: Basic homological lemmas well known for modules over rings and, more generally, in the context of...

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Versal deformation theory of algebras over a quadratic operad

Alice Fialowski, Goutam Mukherjee, Anita Naolekar. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 179--198.Abstract: We develop deformation theory of algebras over quadratic operads...

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Kei modules and unoriented link invariants

Michael Grier, Sam Nelson. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 167--177.Abstract: We define invariants of unoriented knots and links by enhancing the integral kei counting...

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Complexification and homotopy

Wojciech Kucharz, Łukasz Maciejewski. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 159--165.Abstract: Let $Y$ be a real algebraic variety. We are interested in determining the...

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Postnikov towers with fibers generalized Eilenberg-Mac Lane spaces

Kouyemon Iriye, Daisuke Kishimoto. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 139--157.Abstract: A generalized Postnikov tower (GPT) is defined as a tower of principal fibrations...

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The homology graph of a precubical set

Thomas Kahl. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 119--138.Abstract: Precubical sets are used to model concurrent systems. We introduce the homology graph of a precubical...

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Holohonies for connections with values in $L_\infty$-algebras

Camilo Arias Abad, Florian Schätz. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 89--118.Abstract: Given a flat connection $\alpha$ on a manifold $M$ with values in a filtered...

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Note on the homotopy groups of a bouquet $S^1\vee Y$, $Y$ 1-connected

Joseph Roitberg. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 83--87.Abstract: A study is made of the action of the fundamental group of a bouquet of a circle and a 1-connected...

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Free 2-rank of symmetry of products of Milnor manifolds

Mahender Singh. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 65--81.Abstract: A real Milnor manifold is the non-singular hypersurface of degree $(1; 1)$ in the product of two real...

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Simplification of complexes of persistent homology computations

Paweł Dłotko, Hubert Wagner. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 49--63.Abstract: In this paper we focus on preprocessing for persistent homology computations. We adapt...

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Secondy multiplication in Tate cohomology of generalized quaternion groups

Martin Langer. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 27--47.Abstract: Let $k$ be a field, and let $G$ be a finite group. By a theorem of D. Benson, H. Krause, and S....

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Homology operations and cosimplicial iterated loop spaces

Philip Hackney. Source: Homology, Homotopy and Applications, Volume 16, Number 1, 1--25.Abstract: If $X$ is a cosimplical $E_{n+1}$ space then $\operatorname{Tot}(X)$ is an $E_{n+1}$ space and its mod...

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Power maps on $p$-regular Lie groups

Stephen TheriaultSource: Homology Homotopy Appl., Volume 15, Number 2, 83--102.Abstract: A simple, simply-connected, compact Lie group $G$ is $p$-regular if it is homotopy equivalent to a product of...

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