shh.homolalg
Class CochainCx

Object
  CochainCx

All Implemented Interfaces:

ExactCategoryObj, Obj

public abstract class CochainCx

extends Object

implements ExactCategoryObj

A bounded cochain complex with objects in an underlying exact category. CochainMap is not implemented yet.

To use this class, create a subclass that implements the four abstract methods.

Author:

Mark McConnell

Constructor Summary

CochainCx()

Method Summary

boolean	ddIsZero() For testing: returns true if the composition of any two consecutive differentials is zero.
abstract ExactCategoryMorphism	getDiff(int deg) Returns the differential from getObj(deg) to getObj(deg+1).
Morphism	getIdMorphism() Unsupported.
abstract int	getMaxDeg() If i is greater than (>) this value, getObj(i) must be zero.
abstract int	getMinDeg() If i is less than (<) this value, getObj(i) must be zero.
abstract ExactCategoryObj	getObj(int deg) Returns the object in degree deg.
ExactCategoryMorphism	getZeroMorphism(ExactCategoryObj source) Unsupported.
ExactCategoryMorphism	H(int i) Computes the cohomology Hi of this complex, with extra structure.
boolean	isZero() Whether this is a zero object.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

CochainCx

public CochainCx()

Method Detail

getObj

public abstract ExactCategoryObj getObj(int deg)

Returns the object in degree deg. It should not return null.

getDiff

public abstract ExactCategoryMorphism getDiff(int deg)

Returns the differential from getObj(deg) to getObj(deg+1). It should not return null. Two consecutive differentials must have composition zero.

getMinDeg

public abstract int getMinDeg()

If i is less than (<) this value, getObj(i) must be zero. (The converse need not hold.)

getMaxDeg

public abstract int getMaxDeg()

If i is greater than (>) this value, getObj(i) must be zero. (The converse need not hold.)

getIdMorphism

public Morphism getIdMorphism()

Unsupported. We haven't defined CochainMap yet.

Specified by:

getIdMorphism in interface Obj

isZero

public boolean isZero()

Description copied from interface: ExactCategoryObj

Whether this is a zero object.

Specified by:

isZero in interface ExactCategoryObj

getZeroMorphism

public ExactCategoryMorphism getZeroMorphism(ExactCategoryObj source)

Unsupported. We haven't defined CochainMap yet.

Specified by:

getZeroMorphism in interface ExactCategoryObj

H

public ExactCategoryMorphism H(int i)

Computes the cohomology Hⁱ of this complex, with extra structure.

Returns:

A morphism from Hⁱ to getObj(i) that maps each cohomology class to a representative cocycle. To recover the object Hⁱ, use Morphism.getSource().

ddIsZero

public boolean ddIsZero()

For testing: returns true if the composition of any two consecutive differentials is zero.