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Quivers, graph, Continuity a function between 2 topological spaces is…

- - - - A graph is connected iff it has a spanning tree
- - - - Jordan curve theorem
        A simple closed curve in R² defines an inside. This curve with its inside is homeomorphic to D²
- - - - a knot k1 is equivalent to another k2 if it can be cts deformed into it without crossing itself
      - a plane projection of a knot is a knot in 3d viewed on the 2d plane
        the projection is generic if there is a discrete set of double points where the curve crosses itself
        
        Rademeister moves
        2 plane projections of the same knot can be transformed into each other by the 3 Rademeister moves
        
        Rademeister moves preserve tricolorability
        
        the directional writhing number counts the number of over and under passing (resp. +1 and -1) of a knot for a given projection direction
        
        the writhing number is the average over all directions
      - a strand is a part of a knot that goes from an underpass to the next
        
        tricolorability
      - a link is a collection of disjoint knots
        
        a splitting plane for a link is a plane (a 2d plane in R³) which has knots on both semi spaces
        
        a link is splittable if an equivalent link has a splitting plane
        
        equivalence on links is defined as for knots
        
        the linking number is a quantity of a link that depends on the crossing
        
        the linking number is invariant to Rademeister moves
  - - - M is orientable if it has a consistently orientable triangulation.
    - - 2 triangles sharing an edge in a triangulation of a 2 manifold are consistently oriented if their orientation is reversed on that edge.
      - The Euler characteristic is an alternating sum: n-m+l
        = 2 for a sphere
        = 2 - 2g for a sphere with g tubes
        = 2 - g for a sphere with g cross caps
        Independent of the triangulation