Compute the fundamental group the union of two cubes joined at one corner and otherwise disjoint.
Knowing that I have taken only chapter 1 & 2 of " introduction to knot theory " of Richard H. Crowell and Ralph H. Fox.
Which includes the fundamental group of the circle but does not include van Kampen theorem.
Could anyone give me a hint for the solution please?
Notice that a wedge of two cubes is a Hausdorff space, meaning every point is closed. What this means is that in the product with an inteval the wedge point cross the interval is closed. Each cube is also contractible to its corner keeping the corner fixed. Can you use this information to show the wedge of two cubes is contractible?