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Showing 1 to 14 of 14 for “"Hochschild homology"”.
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MOTIVIC HOCHSCHILD HOMOLOGY
… ring spectrum in SH(S); we define the motivic Hochschild homology of R via the derived tensor product: MHH(R)=R ∧_{R ∧ R^{op}} R. This spectrum can be considered the motivic analogue of topological Hochschild homology. The purpose of the first part of this thesis is to investigate the homotopy …
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Topological Hochschild homology of twisted group algebras
… orthogonal spectra ... between the topological Hochschild homology of the group algebra A[G] and the smash product of the topological Hochschild homology of A and the cyclic bar construction of G. This thesis generalizes this result to a twisted group algebra AT[G]. As an A-module, Ar[G] = A[G], …
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Hochschild Homology and De Rham Cohomology of Stratifolds
… called Stratifolds. In this work the de Rham Cohomology and the Hochschild Homology of the algebra of smooth functions on a Stratifold will be computed and a generalization of Alain Connes result about the Hochschild Homology of smooth fuctions on a manifold will be proven.
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Hochschild homology / cohomology of preprojective algebras of ADET quivers
… singularities. In this thesis, I computed the Hochschild homology/cohomology of [Pi]q over C for quivers of type ADET, together with the cup product, and more generally, the calculus structure. It turns out that the Hochschild cohomology also has a Batalin-Vilkovisky structure. I also computed …
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On Using Graphical Calculi: Centers, Zeroth Hochschild Homology and Possible Compositions of Induction and Restriction Functors in Various Diagrammatical Algebras
… and the Moebius band to determine the zeroth Hochschild Homology of Kuperberg's webs for rank two Lie algebras. We use results from Sikora and Westbury to prove the linear independence of these webs on these surfaces. In the third chapter, we use other diagrams to attempt to find explicitely …
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Adams Operations and the Dennis Trace Map
… A, the algebraic K-theory of A, K*(A), and the Hochschild homology of A, HH*(A), are graded rings, and the Dennis trace map D : K *(A) → HH*( A) is a graded ring map. Since Hochschild homology is a more user friendly theory than the algebraic K-theory, one would like to use the Dennis trace …
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From manifolds to invariants of En̳-algebras
… of En-algebras which generalize topological Hochschild homology. The main goal of this thesis is to simply give a definition of those invariants. We define PROPs EG, for G a structure group sitting over GL(n, R). Given a manifold with a (tangential) G-structure, we define functors EG[M]: (EG) …
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The Lefschetz -Reidemeister Trace in Algebraic K -Theory
… of a ring with a bimodule and whose range is the Hochschild homology of the ring with the bimodule. One also recovers the Lefschetz-Nielsen series of the self-map in a similar context. This point of view suggests a natural extension of the notion of the Lefschetz-Reidemeister trace to the higher …
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Symplectic cohomology and duality for the wrapped Fukaya Category
… we show that natural geometric maps from the Hochschild homology of W to symplectic cohomology and from symplectic cohomology to the Hochschild cohomology of W are isomorphisms, in a manner compatible with ring and module structures. This is a consequence of a more general duality for the …
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On Hopf Algebra Type and Rational Calculus Decompositions
… generalizes the decomposition of higher Hochschild homology of Part I. Other examples include the cohomology of loop spaces and the Poincare-Birkhoff Witt theorem for Lie algebras over fields of characteristic zero.
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Noncommutative ring spectra
… We give an explicit construction of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another family of polyhedra called cyclohedra. Using this construction we can then study how THH(A) varies over the moduli space of AO structures on A, a problem which seems …
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A proof of Tsygan's formality conjecture for an arbitrary smooth manifold
… my thesis I propose Fedosov resolutions for the Hochschild cohomological and homological complexes of the algebra of functions on an arbitrary smooth manifold. Using these resolutions together with Kontsevich's formality quasi-isomorphism for Hochschild cochains of R((y1, . . . , yd)) and …
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Knot Floer Homology and Categorification
… understanding the connections between knot homology theories arising from categorification and from Heegaard Floer homology, we present a self-contained construction of knot Floer homology in the language of HOMFLY-PT homology. Using the cube of resolutions for knot Floer homology defined by …
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A Künneth theorem for the cyclic homology of A-infinity algebras
The cyclic homology of a Z/2Z-graded, smooth and proper A-infinity category satisfying the Hodge-to-de-Rham degeneration property carries the structure of a polarized semi-infinite Hodge structure or the so-called EP-structure. Given two A-infinity algebras A and B with the above conditions, we …