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Showing 1 to 18 of 18 for “"Spectral sequences"”.
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Results on spectral sequences for monopole and singular instanton Floer homologies
… [16]. For both cases, we study in particular the spectral sequence that relates the Floer homologies to the Khovanov homologies of links. In our study of singular instanton Floer homology, we introduce a version of Khovanov homology for alternating links with marking data, W, inspired by singular …
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Power Operations In The Kunneth And C_2-Equivariant Adams Spectral Sequences With Applications
<p>We construct Power operations in the K"unneth spectral sequence and the $C_2$ equivariant Adams spectral sequence. While the operations in the K"unneth spectral sequence are 0 in $Tor$, they still detect operations in the target of the spectral sequence. We then interpret these computations of …
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Homología efectiva y sucesiones espectrales
Effective homology and spectral sequences are two different techniques of Algebraic Topology which can be used for the computation of homology and homotopy groups. In this work we try to relate both methods, showing that the effective homology method can also be used to produce algorithms computing …
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Spectral systems: new instances and algorithms
… capable of distinguishing complex spaces. Spectral sequences have long played a central role in this endeavor, providing structured approximations to homological and homotopical invariants. More recently, spectral systems, introduced by Benjamin Matschke, have emerged as a broad …
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Localization and Heegaard Floer Homology
… groups of knots by constructing localization spectral sequences in Heegaard Floer homology.
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Computing the Goodwillie-Taylor tower of discrete modules
… of $D_1F$ is described and the associated spectral sequence is shown to be equivalent to the filtration by rows of the reduced Robinson bicomplex of $F$. We consider the rank filtrations of $P_mF$ and $D_mF$ and give explicit descriptions of the entries of the $E^1$ page of the associated …
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Deformations of homotopy theories via algebraic theories
… and reasoning with obstruction theories and spectral sequences that compute homotopical data starting with purely algebraic data. We investigate the algebra necessary to apply this to examples of interest, such as to E-infinity rings with good theories of power operations. As an application, …
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The Ro (S¹)-graded equivariant homotopy of THH(Fp)
… functors, we provide examples of how Kunneth spectral sequences can be used to understand RO(S¹)-graded TR.
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Andre-Quillen homology for simplicial algebras and ring spectra
… way. We are then further able to construct spectral sequences for Andre-Quillen homology like the spectral sequence for the indecomposables or the Fundamental spectral sequence according to Quillen. The Andre-Quillen homology for algebras constructed as cellular complexes is calculated and …
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The v₁-periodic part of the Adams spectral sequence at an odd prime/
… chromatic height 1 through the lens of the Adams spectral sequence. We find the "dancers to a discordant system." We calculate a Bockstein spectral sequence which converges to the 1-line of the chromatic spectral sequence for the odd primary Adams E₂-page. Furthermore, we calculate the associated …
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Computational methods for higher real K-theory with applications to tmf
… with conjectures as to the collapse of the spectral sequences used herein to compute the homotopy.
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MOTIVIC HOCHSCHILD HOMOLOGY
… (0,-1). To do so, we introduce a tri-graded spectral sequence in motivic homotopy groups inspired by an analogue in stable homotopy theory defined by J. Greenlees in a 2016 paper. We will use our spectral sequence to investigate different spectra. As a motivation for the following …
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Unstable operations in the Bousfield-Kan spectral sequence for simplicial commutative FF₂-algebras
In this thesis we study the Bousfield-Kan spectral sequence (BKSS) in the Quillen model category sCom of simplicial commutative FF₂ -algebras. We develop a theory of unstable operations for this BKSS and relate these operations with the known unstable operations on the homotopy of the target. We …
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On the regular slice spectral sequence
In this thesis, we analyze a variant of the slice spectral sequence of [HHR (or SSS) called the regular slice spectral sequence (or RSSS). This latter spectral sequence is defined using only the regular slice cells. We show that the regular slice tower of a spectrum is just the suspension of the …
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On the infinitesimal theory of Chow groups
… formula follows from the fact that the coniveau spectral sequence for algebraic K-theory on X induces flasque resolutions of these sheaves. Algebraic cycles and algebraic K-theory are thereby related via the general method of coniveau filtration of a topological space. Hence, "linearization" of …
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WEIGHT STRUCTURES AND MOTIVIC COMPARISONS OF P-ADIC COHOMOLOGY THEORIES FOR RIGID ANALYTIC SPACES
… Combining these two aspects, we construct two spectral sequences converging to the Hyodo--Kato cohomology of smooth quasi-compact rigid analytic spaces over Q_p (without reduction assumptions) and to the de Rham--Fargues--Fontaine cohomology of such spaces over C_p. In particular, for a smooth …