SpectralSequences : Table of Contents

• SpectralSequences -- a package for working with filtered complexes and spectral sequences
• A spectral sequence which fails to degenerate quickly
• associatedGradedHomologyObject -- compute the associated graded homology object
• Balancing Tor
• basis(List,SpectralSequencePage) -- generators of a particular degree
• ChainComplex ** FilteredComplex -- filtered tensor product of complexes
• chainComplex(FilteredComplex) -- the ambient chain complex of a filtered complex
• chainComplex(SpectralSequence) -- the underlying chain complex of a Spectral Sequence
• Computing the Serre Spectral Sequence associated to a Hopf Fibration
• connectingMorphism -- use spectral sequences to compute connecting morphisms
• connectingMorphism(ChainComplexMap,ZZ) -- use spectral sequences to compute connecting morphisms
• degree(Page)
• describe(Page) -- real description
• describe(PageMap) -- real description
• describe(SpectralSequence) -- real description
• describe(SpectralSequencePage) -- real description
• describe(SpectralSequencePageMap) -- real description
• Edge homomorphisms
• edgeComplex -- the edge homomorphisms
• Example 1 -- Easy example of a filtered simplicial complex
• Example 2 -- Easy example of a filtered simplicial complex
• Example 3 -- Easy example of a filtered simplicial complex
• Examples of change of rings Spectral Sequences
• Examples of filtered complexes and spectral sequences -- How to use this package
• expression(SpectralSequence)
• Filtered complexes and simplicial complexes
• filtered complexes and spectral sequences from simplicial complexes
• FilteredComplex -- the type of all filtered complexes
• filteredComplex -- make a filtered complex
• FilteredComplex ^ ZZ -- the filtered pieces
• FilteredComplex _ ZZ -- the filtered pieces
• filteredComplex(...,ReducedHomology=>...)
• filteredComplex(...,Shift=>...)
• filteredComplex(ChainComplex) -- obtain a filtered complex from a chain complex
• filteredComplex(Ideal,ChainComplex,ZZ) -- I-adic filtrations of chain complexes
• filteredComplex(List) -- obtain a filtered complex from a list of chain complex maps or a nested list of simplicial complexes
• filteredComplex(SpectralSequence) -- obtain the filtered complex associated to the spectral sequence
• filteredHomologyObject -- compute the filtered homology object
• filteredHomologyObject(ZZ,ZZ,FilteredComplex) -- compute the filtered homology object
• Filtrations and homomorphism complexes
• Filtrations and tensor product complexes
• hilbertPolynomial(SpectralSequencePage) -- the Hilbert polynomial of a spectral sequence page
• Hom(FilteredComplex,ChainComplex) -- the filtered Hom complex
• homologyIsomorphism -- compute the homology isomorphism
• homologyIsomorphism(SpectralSequence,ZZ,ZZ,ZZ) -- the homology isomorphism
• How to make filtered complexes from chain complex maps
• I-adic filtrations of chain complexes and their spectral sequences
• Identifying anti-podal points of the two sphere
• inducedMap(FilteredComplex,ZZ) -- the i th inclusion map in a filtered complex
• max(FilteredComplex) -- maximum spot where the given filtered complex has a module.
• min(FilteredComplex) -- minimum spot where the given filtered complex has a module.
• minimalPresentation(SpectralSequence) -- a minimal presentation of a spectral sequence
• minimalPresentation(SpectralSequencePage) -- a minimal presentation of a spectral sequence page
• net(FilteredComplex)
• net(Page)
• net(PageMap)
• net(SpectralSequence)
• net(SpectralSequencePage)
• netPage -- display a small portion of a given Spectral Sequence page
• new Page
• Page -- the type of all pages
• page
• Page _ List
• page(...,Prune=>...)
• page(SpectralSequencePage)
• PageMap -- the type of all page maps
• pageMap
• PageMap _ List
• pruningMaps -- compute the pruning maps on a spectral sequence page
• pruningMaps(SpectralSequencePage) -- compute the pruning maps on a spectral sequence page
• ReducedHomology -- name for an optional argument
• ring(Page)
• Seeing Cancellations
• Shift -- name for an optional argument
• sourcePruningMap
• Spectral sequences and connecting morphisms
• Spectral sequences and hypercohomology calculations
• Spectral sequences and non-Koszul syzygies
• SpectralSequence -- the type of all spectral sequences
• spectralSequence -- construct a spectral sequence
• SpectralSequence ^ InfiniteNumber -- the infinity page of a spectral sequence
• SpectralSequence ^ ZZ -- the kth page of a spectral sequence
• SpectralSequence _ ZZ -- the kth page of a spectral sequence
• spectralSequence(...,Prune=>...)
• spectralSequence(FilteredComplex) -- construct a spectral sequence from a filtered complex
• SpectralSequencePage -- the type of all spectral sequence pages
• spectralSequencePage -- construct a spectral sequence page from a filtered complex
• SpectralSequencePage ^ List -- the module in the i,j position on the page
• SpectralSequencePage _ List -- the module in the i,j position on the page
• spectralSequencePage(...,Prune=>...)
• spectralSequencePage(FilteredComplex,ZZ) -- construct a spectral sequence page from a filtered complex
• SpectralSequencePageMap -- the type of all spectral sequence page maps
• spectralSequencePageMap -- compute the maps on a spectral sequence page
• SpectralSequencePageMap ^ List -- the p,q th map on of a spectral sequence page
• SpectralSequencePageMap _ List -- The p,q th map on of a spectral sequence page
• spectralSequencePageMap(...,Prune=>...)
• spots -- which spots does the given page has a module.
• spots(ChainComplex) -- which spots does the given chain complex has a module.
• spots(FilteredComplex) -- which spots does the given filtered complex has a module.
• spots(PageMap)
• support(ChainComplex) -- nonzero parts of a chain complex
• support(FilteredComplex)
• support(Page) -- which non-zero modules appear in the given page.
• support(PageMap)
• support(SpectralSequencePage)
• targetPruningMap
• tensor(RingMap,ChainComplex) -- tensor product of a chain complex by a ring map
• The fibration of the Klein Bottle over the sphere with fibers the sphere
• The trivial fibration over the sphere with fibers the sphere
• truncate(ChainComplex,ZZ) -- compute the hard truncation of a chain complex