Point.hpp File Reference

Contains the methods computing the RO(G) homology of a point. More...

#include "Products/Massey.hpp"
#include "Chain_Complexes/Morse.hpp"
#include "impl/Point.ipp"

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Namespaces
	mackey
	Everything in this library is under this namespace.

Functions
template<typename T , typename deg_t = std::vector<int>>
int	dimension (const deg_t &sphere)
	Compute the dimension of a representation sphere. More...
template<typename T , typename deg_t = std::vector<int>>
deg_t	Reindex (deg_t degree)
	Given degree (k,sphere) returns degree (k',sphere) where k' is a reindexing of k s.t. 0<=k'<=dimension(sphere) More...
template<typename T , typename deg_t = std::vector<int>>
deg_t	invReindex (deg_t degree)
	Inverse of Reindex. More...
template<typename T , typename deg_t = std::vector<int>>
auto	getChains (const deg_t &sphere, int i=-1)
	Returns the standard Chains of the given sphere. Optionally stop at index i (i=-1 means nonstop i.e. i=dimension(sphere) ) More...
template<typename group_t , typename deg_t >
auto	ROChains (const deg_t &sphere, int i=-1)
	Returns the Chains of given sphere. Optionally stop at index i (i=-1 means nonstop i.e. i=dimension(sphere) ) More...
template<typename group_t >
auto	HomologyLevels (const Levels< Junction< typename group_t::rank_t, typename group_t::diff_t >, group_t > &J)
	The Mackey functor Homology of a Junction of Mackey functors. More...
template<typename group_t , typename deg_t = std::vector<int>>
auto	ROHomology (int level, const deg_t &degree)
	Computes the homology for the given level and degree. More...
template<typename group_t , typename deg_t = std::vector<int>>
auto	ROHomology (const deg_t &sphere)
	Computes the Mackey functor homology of the given sphere. More...
template<typename group_t , typename deg_t = std::vector<int>>
auto	ROGreen (int level, const deg_t &first, const deg_t &second, int selectFirst=0, int selectSecond=0)
	Computes the product of two generators in the RO(G) homology given their level, degrees and selections (if noncyclic). Selections are 0,0 by default. More...
template<typename group_t , typename deg_t = std::vector<int>>
Massey< group_t >	ROMassey (int level, const deg_t &first, const deg_t &second, const deg_t &third, int selectFirst=0, int selectSecond=0, int selectThird=0)
	Computes the Massey product of three generators in the RO(G) homology given their level, degrees and selections (if noncyclic). Selections are 0,0,0 by default. More...

Detailed Description

Contains the methods computing the RO(G) homology of a point.

That includes the additive (Mackey functor) and multiplicative (Green functor) structures and Massey products.