scholarly journals Bordered Floer homology and the spectral sequence of a branched double cover II: the spectral sequences agree

2016 ◽  
Vol 9 (2) ◽  
pp. 607-686
Author(s):  
Robert Lipshitz ◽  
Peter S. Ozsváth ◽  
Dylan P. Thurston
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Double Cover ◽  
Spectral Sequences

scholarly journals Bordered Floer homology and the spectral sequence of a branched double cover I

2014 ◽  
Vol 7 (4) ◽  
pp. 1155-1199 ◽  
Author(s):  
Robert Lipshitz ◽  
Peter S. Ozsváth ◽  
Dylan P. Thurston
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Double Cover

scholarly journals Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Antieau ◽  
Bhargav Bhatt ◽  
Akhil Mathew
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Characteristic P ◽  
De Rham

Abstract We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

Motivic cohomology of quadrics and the coniveau spectral sequence

2010 ◽  
Vol 6 (3) ◽  
pp. 547-589 ◽  
Author(s):  
Nobuaki Yagita
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Motivic Cohomology

AbstractWe study the coniveau spectral sequence for quadrics defined by Pfister forms. In particular, we explicitly compute the motivic cohomology of anisotropic quadrics over ℝ, by showing that their coniveau spectral sequences collapse from the -term

Spectral Sequences

2020 ◽  
pp. 45-56
Author(s):  
Loring W. Tu
Keyword(s):  
Projective Plane ◽  
Spectral Sequence ◽  
Fiber Bundles ◽  
Spectral Sequences ◽  
Complex Projective Plane ◽  
Computational Tool ◽  
Short Introduction ◽  
Complex Projective

This chapter focuses on spectral sequences. The spectral sequence is a powerful computational tool in the theory of fiber bundles. First introduced by Jean Leray in the 1940s, it was further refined by Jean-Louis Koszul, Henri Cartan, Jean-Pierre Serre, and many others. The chapter provides a short introduction, without proofs, to spectral sequences. As an example, it computes the cohomology of the complex projective plane. The chapter then details Leray's theorem. A spectral sequence is like a book with many pages. Each time one turns a page, one obtains a new page that is the cohomology of the previous page.

scholarly journals Model category structures and spectral sequences

2019 ◽  
Vol 150 (6) ◽  
pp. 2815-2848
Author(s):  
Joana Cirici ◽  
Daniela Egas Santander ◽  
Muriel Livernet ◽  
Sarah Whitehouse
Keyword(s):  
Spectral Sequence ◽  
Commutative Ring ◽  
Model Category ◽  
Spectral Sequences ◽  
Model Structures

AbstractLet R be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of R-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a quasi-isomorphism at a certain fixed stage of the associated spectral sequence. For filtered complexes, we relate the different model structures obtained, when we vary the stage of the spectral sequence, using the functors shift and décalage.

scholarly journals ON KNOT FLOER HOMOLOGY FOR SOME FIBERED KNOTS

2013 ◽  
Vol 15 (01) ◽  
pp. 1250053
Author(s):  
LAWRENCE ROBERTS
Keyword(s):  
Floer Homology ◽  
Double Cover ◽  
Knot Floer Homology ◽  
Fibered Knots ◽  
Exact Sequences

We use knot Floer surgery exact sequences and torsion invariants to compute the knot Floer homology of certain fibered knots in the double cover of S3 branched along the closure of an alternating braid.

scholarly journals Volume growth in the component of fibered twists

2018 ◽  
Vol 20 (08) ◽  
pp. 1850014 ◽  
Author(s):  
Joontae Kim ◽  
Myeonggi Kwon ◽  
Junyoung Lee
Keyword(s):  
Lower Bound ◽  
Symplectic Manifold ◽  
Infinite Order ◽  
Floer Homology ◽  
Volume Growth ◽  
Spectral Sequences ◽  
Connected Component ◽  
Text Type ◽  
Infinite Dimensional ◽  
Homology Groups

For a Liouville domain [Formula: see text] whose boundary admits a periodic Reeb flow, we can consider the connected component [Formula: see text] of fibered twists. In this paper, we investigate an entropy-type invariant, called the slow volume growth, in the component [Formula: see text] and give a uniform lower bound of the growth using wrapped Floer homology. We also show that [Formula: see text] has infinite order in [Formula: see text] if there is an admissible Lagrangian [Formula: see text] in [Formula: see text] whose wrapped Floer homology is infinite dimensional. We apply our results to fibered twists coming from the Milnor fibers of [Formula: see text]-type singularities and complements of a symplectic hypersurface in a real symplectic manifold. They admit so-called real Lagrangians, and we can explicitly compute wrapped Floer homology groups using a version of Morse–Bott spectral sequences.

scholarly journals Koszul complexes and spectral sequences associated with Lie algebroids

2020 ◽  
Author(s):  
Ugo Bruzzo ◽  
Vladimir N. Rubtsov
Keyword(s):  
Spectral Sequence ◽  
Complex Manifold ◽  
Global Section ◽  
Koszul Complex ◽  
Inner Product ◽  
Closed Field ◽  
Spectral Sequences ◽  
Lie Algebroid ◽  
Atiyah Algebroid ◽  
Regular Scheme

AbstractWe study some spectral sequences associated with a locally free $${{\mathscr {O}}}_X$$ O X -module $${{\mathscr {A}}}$$ A which has a Lie algebroid structure. Here X is either a complex manifold or a regular scheme over an algebraically closed field k. One spectral sequence can be associated with $${{\mathscr {A}}}$$ A by choosing a global section V of $${{\mathscr {A}}}$$ A , and considering a Koszul complex with a differential given by inner product by V. This spectral sequence is shown to degenerate at the second page by using Deligne’s degeneracy criterion. Another spectral sequence we study arises when considering the Atiyah algebroid $${{{\mathscr {D}}}_{{{\mathscr {E}}}}}$$ D E of a holomolorphic vector bundle $${{\mathscr {E}}}$$ E on a complex manifold. If V is a differential operator on $${{\mathscr {E}}}$$ E with scalar symbol, i.e, a global section of $${{{\mathscr {D}}}_{{{\mathscr {E}}}}}$$ D E , we associate with the pair $$({{\mathscr {E}}},V)$$ ( E , V ) a twisted Koszul complex. The first spectral sequence associated with this complex is known to degenerate at the first page in the untwisted ($${{\mathscr {E}}}=0$$ E = 0 ) case.

scholarly journals Spectral sequences for commutative Lie algebras

2020 ◽  
Vol 28 (2) ◽  
pp. 123-137
Author(s):  
Friedrich Wagemann
Keyword(s):  
Spectral Sequence ◽  
Lie Algebras ◽  
Spectral Sequences ◽  
Characteristic 2 ◽  
Leibniz Cohomology

AbstractWe construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic 2. In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley--Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.

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