Displaying similar documents to “A note on product structures on Hochschild homology of schemes”

Homological computations in the universal Steenrod algebra

A. Ciampella, L. A. Lomonaco (2004)

Fundamenta Mathematicae

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We study the (bigraded) homology of the universal Steenrod algebra Q over the prime field ₂, and we compute the groups H s , s ( Q ) , s ≥ 0, using some ideas and techniques of Koszul algebras developed by S. Priddy in [5], although we presently do not know whether or not Q is a Koszul algebra. We also provide an explicit formula for the coalgebra structure of the diagonal homology D ( Q ) = s 0 H s , s ( Q ) and show that D⁎(Q) is isomorphic to the coalgebra of invariants Γ introduced by W. Singer in [6].

Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers

Robert Lipshitz, David Treumann (2016)

Journal of the European Mathematical Society

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Let A be a dg algebra over 𝔽 2 and let M be a dg A -bimodule. We show that under certain technical hypotheses on A , a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product M A L M and converges to the Hochschild homology of M . We apply this result to bordered Heegaard Floer theory, giving spectral sequences associated to Heegaard Floer homology groups of certain branched and unbranched double covers.

A faithful linear-categorical action of the mapping class group of a surface with boundary

Robert Lipshitz, Peter Ozsváth, Dylan P. Thurston (2013)

Journal of the European Mathematical Society

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We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin c -structure is faithful. This paper is designed partly as an introduction to the subject, and much of it should be readable without a background in Floer homology.

Torsion of Khovanov homology

Alexander N. Shumakovitch (2014)

Fundamenta Mathematicae

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Khovanov homology is a recently introduced invariant of oriented links in ℝ³. It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic of Khovanov homology is a version of the Jones polynomial for links. In this paper we study torsion of Khovanov homology. Based on our calculations, we formulate several conjectures about the torsion and prove weaker versions of the first two of them. In particular, we prove that all non-split alternating links have their...

Injective comodules and Landweber exact homology theories

Mark Hovey (2007)

Fundamenta Mathematicae

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We classify the indecomposable injective E(n)⁎E(n)-comodules, where E(n) is the Johnson-Wilson homology theory. They are suspensions of the J n , r = E ( n ) ( M r E ( r ) ) , where 0 ≤ r ≤ n, with the endomorphism ring of J n , r being E ( r ) ^ * E ( r ) ^ , where E ( r ) ^ denotes the completion of E(r).

Transverse Homology Groups

S. Dragotti, G. Magro, L. Parlato (2006)

Bollettino dell'Unione Matematica Italiana

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We give, here, a geometric treatment of intersection homology theory.

On the geometry of polynomial mappings at infinity

Anna Valette, Guillaume Valette (2014)

Annales de l’institut Fourier

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We associate to a given polynomial map from 2 to itself with nonvanishing Jacobian a variety whose homology or intersection homology describes the geometry of singularities at infinity of this map.

Waldhausen’s Nil groups and continuously controlled K-theory

Hans Munkholm, Stratos Prassidis (1999)

Fundamenta Mathematicae

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Let Γ = Γ 1 * G Γ 2 be the pushout of two groups Γ i , i = 1,2, over a common subgroup G, and H be the double mapping cylinder of the corresponding diagram of classifying spaces B Γ 1 B G B Γ 2 . Denote by ξ the diagram I p H 1 X = H , where p is the natural map onto the unit interval. We show that the N i l groups which occur in Waldhausen’s description of K * ( Γ ) coincide with the continuously controlled groups * c c ( ξ ) , defined by Anderson and Munkholm. This also allows us to identify the continuously controlled groups * c c ( ξ + ) which are known to form...