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I would like to get topological information about the complement of two lines, which intersect in a point, in 3-space. I have come across this considering deformations of discontinuous groups for the Heisenberg group and have never thought much about knot theory. Could someone point me to a reference or give me a quick overview of how such spaces are studied topologically?

The Google search pages seem to refer to braid groups and knot theory, but I am not sure whether this is directly relevant to complements of intersecting lines.

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Isn't this thing homotopy equivalent to a wedge of three circles? Probably I'm just being silly, it's hard for me to visualize :) – Dylan Wilson Jun 16 at 7:07
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 Center a sphere at the intersection point and deformation-retract your space to its intersection with it. It looks like math.stackexchange.com is a better place to ask this sort of questions, by the way. – Mariano Suárez-Alvarez Jun 16 at 7:08
This deformation-retracts radially to a $2$-sphere minus $4$ points. – Douglas Zare Jun 16 at 7:09
Which is, in turn, homotopy equivalent to a wedge of three circles, right? – Dylan Wilson Jun 16 at 7:15
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 Thank you for the quick answer & apologies if my question was off-topic. – s.barmeier Jun 16 at 7:29
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closed as off topic by Douglas Zare, Chandan Singh Dalawat, s.barmeier, Mark Grant, Dan Petersen Jun 16 at 8:14

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