A How Does Induced Mapping Function in Algebraic Topology?

  • A
  • Thread starter Thread starter srgmath2905
  • Start date Start date
  • Tags Tags
    Induced Mapping
srgmath2905
Messages
1
Reaction score
2
Given example for what is induced mapping ? In basic level
 
Physics news on Phys.org
srgmath2905 said:
Given example for what is induced mapping ? In basic level
Without context this is impossible to answer. The same term is used differently in different contexts.
 
Maybe only commonality is that it's functorial in nature *
*As well as in the wild ;).
Edit: In Algebraic Topology, given f: X-->Y, and groups G/N in X, G'/N' in Y( some (co) homology or Homotopy groups associated to each of X,Y, with N normal in G. N' normal in G), often designated as i* I believe they're of the form:
i*([a])=([f([a])]), from G/N to G'/N'. So a map between cosets.

So, e.g., the homotopy class [a] of ## \pi_1(X)## as above, is sent to the class [f(a)] in ##\pi_1(Y)##.
 
Last edited:
Thread 'Determine whether ##125## is a unit in ##\mathbb{Z_471}##'
This is the question, I understand the concept, in ##\mathbb{Z_n}## an element is a is a unit if and only if gcd( a,n) =1. My understanding of backwards substitution, ... i have using Euclidean algorithm, ##471 = 3⋅121 + 108## ##121 = 1⋅108 + 13## ##108 =8⋅13+4## ##13=3⋅4+1## ##4=4⋅1+0## using back-substitution, ##1=13-3⋅4## ##=(121-1⋅108)-3(108-8⋅13)## ... ##= 121-(471-3⋅121)-3⋅471+9⋅121+24⋅121-24(471-3⋅121## ##=121-471+3⋅121-3⋅471+9⋅121+24⋅121-24⋅471+72⋅121##...

Similar threads

Back
Top