I am interested to learn more about algebraic topology. At the higher levels, which parts of algebraic topology are more "discrete", i.e. does not deal as much with limits/tangent spaces/differentials, etc?
I am a beginner at this (still at the level of Hatcher's book), with a strong preference for "discrete" math, e.g. prefer algebra over analysis.
I am ok with learning the fundamentals of both "discrete" and "continuous" (e.g. Hatcher's book, Munkres topology), but for higher levels beyond that, which field should I look to if I want to study more "discrete" type of topology?
Some examples of types of topology that seems "continuous" to me would be for instance, Differentiable Manifolds, Topology of Lie Groups, etc.
Some examples of types of topology that seems more "discrete" would be simplicial homotopy, braid theory, etc.
Any other examples? Hope this questions makes sense (I am not an expert).
Thanks for any help.