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  • ...=q(a)</math>, and <math>g(0,b)=g(1,b)=x</math>. We call <math>g</math> a [[homotopy]]. Now define <math>\pi_1(X)=L/\sim</math>. That is, we equate any two elem == Higher Homotopy Groups ==
    3 KB (479 words) - 14:35, 1 December 2015
  • ...re to any positive integer ''n'', stating that a compact ''n'' manifold is homotopy equivalent to the ''n'' sphere [[iff]] it is homeomorphic to the ''n'' sphe
    13 KB (1,969 words) - 16:57, 22 February 2024
  • ...(X,x_0)</math> by saying that <math>f\sim g</math> if there is a (based) [[homotopy]] between <math>f</math> and <math>g</math> (that is, if there is a continu ...py from <math>a</math> to <math>a'</math>, then <math>f\circ F</math> is a homotopy from <math>f\circ a</math> to <math>f\circ a'</math>), and thus <math>f_*</
    8 KB (1,518 words) - 19:11, 23 January 2017