Mackey  V3.3
A C++ library for computing RO(G) graded homology
Point.hpp
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1 #pragma once
2 #include "Products/Massey.hpp"
3 #include "Chain_Complexes/Morse.hpp"
4 
8 
9 namespace mackey {
10 
11 
13  template<typename T, typename deg_t = std::vector<int>>
14  int dimension(const deg_t& sphere);
15 
17  template<typename T, typename deg_t = std::vector<int>>
18  deg_t Reindex(deg_t degree);
20  template<typename T, typename deg_t = std::vector<int>>
21  deg_t invReindex(deg_t degree);
22 
24  template<typename T, typename deg_t = std::vector<int>>
25  auto getChains(const deg_t& sphere, int i = -1);
26 
28  template<typename group_t, typename deg_t>
29  auto ROChains(const deg_t& sphere, int i = -1);
30 
32  template<typename group_t>
33  auto HomologyLevels(const Levels<Junction<typename group_t::rank_t, typename group_t::diff_t>, group_t >& J);
34 
36  template<typename group_t, typename deg_t = std::vector<int> >
37  auto ROHomology(int level, const deg_t& degree);
38 
40  template<typename group_t, typename deg_t = std::vector<int>>
41  auto ROHomology(const deg_t& sphere);
42 
44  template<typename group_t, typename deg_t = std::vector<int>>
45  auto ROGreen(int level, const deg_t& first, const deg_t& second, int selectFirst = 0, int selectSecond = 0);
46 
48  template<typename group_t, typename deg_t = std::vector<int>>
49  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);
50 }
51 #include "impl/Point.ipp"
Massey.hpp
Contains the classes mackey::Massey and mackey::internal::MasseyCompute.
Morse.hpp
Contains the classes mackey::AMT and mackey::EquivariantAMT.
mackey::Junction
Consisting of an entering and an exiting differential.
Definition: Chains.hpp:69
mackey::Massey
Stores Massey products and their indeterminacy.
Definition: Massey.hpp:11
mackey
Everything in this library is under this namespace.
Definition: Box.hpp:9
mackey::ROChains
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....
mackey::ROMassey
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,...
mackey::Reindex
deg_t Reindex(deg_t degree)
Given degree (k,sphere) returns degree (k',sphere) where k' is a reindexing of k s....
mackey::dimension
int dimension(const deg_t &sphere)
Compute the dimension of a representation sphere.
mackey::HomologyLevels
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.
mackey::getChains
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....
mackey::invReindex
deg_t invReindex(deg_t degree)
Inverse of Reindex.
mackey::ROGreen
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 selection...
mackey::ROHomology
auto ROHomology(int level, const deg_t &degree)
Computes the homology for the given level and degree.
mackey::Levels
Storage of various levels of Junction/Chains.
Definition: Levels.hpp:23