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Unformatted text preview: (4) The boundary of the disk, D 2 := { x ∈ R 2  x  < 1 } , is a circle, as is the boundary of the Mobius band. What surfaces do we get when we glue the disk to itself, the disk to a Mobius band, and a Mobius band to itself along these circle boundaries? Are there distinct ways to glue these pieces together? Give an argument using pictures discussed in class. Also give an argument for why such gluings actually yield a surface (starting from the deﬁnition of surface given in class). (5) Prove Kan Kampen’s theorem. (See Hatcher for the statement of the theorem and its proof.) 1...
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This note was uploaded on 05/04/2011 for the course MATH 73 taught by Professor Danberwick during the Spring '09 term at Berkeley.
 Spring '09
 DANBERWICK
 Math, Division

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