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Displaying similar documents to “Algebraic K -theory of the first Morava K -theory”

Rational BV-algebra in string topology

Yves Félix, Jean-Claude Thomas (2008)

Bulletin de la Société Mathématique de France

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Let M be a 1-connected closed manifold of dimension m and L M be the space of free loops on M . M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of L M , H * ( L M ; k ) . When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology H H * ( C * ( M ) ; C * ( M ) ) which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between H H * ( C * ( M ) ; C * ( M ) ) and the shifted homology H * + m ( L M ; k ) . We also prove...

Annihilators of local homology modules

Shahram Rezaei (2019)

Czechoslovak Mathematical Journal

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Let ( R , 𝔪 ) be a local ring, 𝔞 an ideal of R and M a nonzero Artinian R -module of Noetherian dimension n with hd ( 𝔞 , M ) = n . We determine the annihilator of the top local homology module H n 𝔞 ( M ) . In fact, we prove that Ann R ( H n 𝔞 ( M ) ) = Ann R ( N ( 𝔞 , M ) ) , where N ( 𝔞 , M ) denotes the smallest submodule of M such that hd ( 𝔞 , M / N ( 𝔞 , M ) ) < n . As a consequence, it follows that for a complete local ring ( R , 𝔪 ) all associated primes of H n 𝔞 ( M ) are minimal.

Taylor towers of symmetric and exterior powers

Brenda Johnson, Randy McCarthy (2008)

Fundamenta Mathematicae

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We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, D k S p and D k Λ , in terms of the first terms in the Taylor towers of S p t and Λ t for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of S p t and Λ t . We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for D k S p and D k Λ .

Coxeter elements for vanishing cycles of types  A 1 2  and  D 1 2

Kyoji Saito (2011)

Annales de l’institut Fourier

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We introduce two entire functions f A 1 2 and f D 1 2 in two variables. Both of them have only two critical values 0 and 1 , and the associated maps C 2 C define topologically locally trivial fibrations over C { 0 , 1 } . All critical points in the singular fibers over 0 and 1 are ordinary double points, and the associated vanishing cycles span the middle homology group of the general fiber, whose intersection diagram forms bi-partitely decomposed infinite quivers of type A 1 2 and D 1 2 , respectively. Coxeter elements...

Topology of Fatou components for endomorphisms of k : linking with the Green’s current

Suzanne Lynch Hruska, Roland K. W. Roeder (2010)

Fundamenta Mathematicae

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Little is known about the global topology of the Fatou set U(f) for holomorphic endomorphisms f : k k , when k >1. Classical theory describes U(f) as the complement in k of the support of a dynamically defined closed positive (1,1) current. Given any closed positive (1,1) current S on k , we give a definition of linking number between closed loops in k s u p p S and the current S. It has the property that if lk(γ,S) ≠ 0, then γ represents a non-trivial homology element in H ( k s u p p S ) . As an application, we use...

Realizable Galois module classes over the group ring for non abelian extensions

Nigel P. Byott, Bouchaïb Sodaïgui (2013)

Annales de l’institut Fourier

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Given an algebraic number field k and a finite group Γ , we write ( O k [ Γ ] ) for the subset of the locally free classgroup Cl ( O k [ Γ ] ) consisting of the classes of rings of integers O N in tame Galois extensions N / k with Gal ( N / k ) Γ . We determine ( O k [ Γ ] ) , and show it is a subgroup of Cl ( O k [ Γ ] ) by means of a description using a Stickelberger ideal and properties of some cyclic codes, when k contains a root of unity of prime order p and Γ = V C , where V is an elementary abelian group of order p r and C is a cyclic group of order m &gt; 1 acting faithfully...

On the unit group of a semisimple group algebra 𝔽 q S L ( 2 , 5 )

Rajendra K. Sharma, Gaurav Mittal (2022)

Mathematica Bohemica

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We give the characterization of the unit group of 𝔽 q S L ( 2 , 5 ) , where 𝔽 q is a finite field with q = p k elements for prime p > 5 , and S L ( 2 , 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group 5 .

Noncommutative numerical motives, Tannakian structures, and motivic Galois groups

Matilde Marcolli, Gonçalo Tabuada (2016)

Journal of the European Mathematical Society

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In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum ( k ) F of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum ( k ) F is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined...

A countably cellular topological group all of whose countable subsets are closed need not be -factorizable

Mihail G. Tkachenko (2023)

Commentationes Mathematicae Universitatis Carolinae

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We construct a Hausdorff topological group G such that 1 is a precalibre of G (hence, G has countable cellularity), all countable subsets of G are closed and C -embedded in G , but G is not -factorizable. This solves Problem 8.6.3 from the book “Topological Groups and Related Structures" (2008) in the negative.

A Riemann-Roch theorem for dg algebras

François Petit (2013)

Bulletin de la Société Mathématique de France

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Given a smooth proper dg algebra A , a perfect dg A -module M and an endomorphism f of M , we define the Hochschild class of the pair ( M , f ) with values in the Hochschild homology of the algebra A . Our main result is a Riemann-Roch type formula involving the convolution of two such Hochschild classes.

Hardness of embedding simplicial complexes in d

Jiří Matoušek, Martin Tancer, Uli Wagner (2011)

Journal of the European Mathematical Society

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Let 𝙴𝙼𝙱𝙴𝙳 k d be the following algorithmic problem: Given a finite simplicial complex K of dimension at most k , does there exist a (piecewise linear) embedding of K into d ? Known results easily imply polynomiality of 𝙴𝙼𝙱𝙴𝙳 k 2 ( k = 1 , 2 ; the case k = 1 , d = 2 is graph planarity) and of 𝙴𝙼𝙱𝙴𝙳 k 2 k for all k 3 . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that 𝙴𝙼𝙱𝙴𝙳 d d and 𝙴𝙼𝙱𝙴𝙳 ( d - 1 ) d are undecidable for each d 5 . Our main result is NP-hardness of 𝙴𝙼𝙱𝙴𝙳 2 4 and, more generally, of 𝙴𝙼𝙱𝙴𝙳 k d for all...

Algebraic and topological properties of some sets in ℓ₁

Taras Banakh, Artur Bartoszewicz, Szymon Głąb, Emilia Szymonik (2012)

Colloquium Mathematicae

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For a sequence x ∈ ℓ₁∖c₀₀, one can consider the set E(x) of all subsums of the series n = 1 x ( n ) . Guthrie and Nymann proved that E(x) is one of the following types of sets: () a finite union of closed intervals; () homeomorphic to the Cantor set; homeomorphic to the set T of subsums of n = 1 b ( n ) where b(2n-1) = 3/4ⁿ and b(2n) = 2/4ⁿ. Denote by ℐ, and the sets of all sequences x ∈ ℓ₁∖c₀₀ such that E(x) has the property (ℐ), () and ( ), respectively. We show that ℐ and are strongly -algebrable and is -lineable....

Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant

Gwénaël Massuyeau (2012)

Bulletin de la Société Mathématique de France

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Let Σ be a compact connected oriented surface with one boundary component, and let π be the fundamental group of Σ . The Johnson filtration is a decreasing sequence of subgroups of the Torelli group of Σ , whose k -th term consists of the self-homeomorphisms of Σ that act trivially at the level of the k -th nilpotent quotient of π . Morita defined a homomorphism from the k -th term of the Johnson filtration to the third homology group of the k -th nilpotent quotient of π . In this paper, we...

Bicrossed products of generalized Taft algebra and group algebras

Dingguo Wang, Xiangdong Cheng, Daowei Lu (2022)

Czechoslovak Mathematical Journal

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Let G be a group generated by a set of finite order elements. We prove that any bicrossed product H m , d ( q ) k [ G ] between the generalized Taft algebra H m , d ( q ) and group algebra k [ G ] is actually the smash product H m , d ( q ) k [ G ] . Then we show that the classification of these smash products could be reduced to the description of the group automorphisms of G . As an application, the classification of H m , d ( q ) k [ C n 1 × C n 2 ] is completely presented by generators and relations, where C n denotes the n -cyclic group.

On n -thin dense sets in powers of topological spaces

Adam Bartoš (2016)

Commentationes Mathematicae Universitatis Carolinae

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A subset of a product of topological spaces is called n -thin if every its two distinct points differ in at least n coordinates. We generalize a construction of Gruenhage, Natkaniec, and Piotrowski, and obtain, under CH, a countable T 3 space X without isolated points such that X n contains an n -thin dense subset, but X n + 1 does not contain any n -thin dense subset. We also observe that part of the construction can be carried out under MA.