## homotopy type of subspace arrangement

I am considering the following problem: let E1,E2,E3,E4 be an orthonormal basis of R^4 what is the homotopy type of
R^4 minus (span{E1,E3} U span{E1,E4} U span{E2,E3} U span{E2,E4})

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Why do you want to know? that is: is this a question where you've observed what the answer is in dimension 3, and want to generalise? Would an answer to this question help you with some computation in group cohomology? If this is just a question someone else has asked you, I feel it would be good manners for you to say so when writing your question. – Yemon Choi Dec 9 2009 at 2:44
-1, needs motivation, etc. (I get a wedge of circles, by the way) – S. Carnahan Dec 9 2009 at 3:12
hi,scott Carnahan,would you explain your idea. – sinbad Dec 9 2009 at 3:29
The complement of those 4 2-planes retracts to its intersection with the 3-sphere, which is the complement of 4 1-spheres chained in a loop. Projecting that intersection to R^3 stereoraphically from a point of intersection of two of the 1-spheres reduces us to consider the complement two lines, and two round 1-spheres with appropriate intersections. Seeing what wedge of circles that retracts to is easy on a picture. – Mariano Suárez-Alvarez Dec 9 2009 at 3:29
i agree with yemen, this feels like a hw problem. Mariano, why didnt you post that as an answer? – Sean Tilson Mar 13 2010 at 19:56