First Exam AA - Columbia Universitybayer/S02/knots/midterm1.pdfFirst Exam AA Surfaces and Knots,...

First Exam AA

Surfaces and Knots, Dave Bayer, February 21, 2002

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You may use scratch paper, but only this sheet will be graded; please present allanswers on this sheet.

[1] Finish labeling the gluing diagram on the right, so it glues together to form the surfaceon the left. Compute the Euler characteristic of this surface.



[4] Determine what surface each of the following gluing diagrams represents, by computingits Euler characteristic, and determining whether it is orientable or not.

[5] Find a pair of gluing diagrams, above, which represent the same surface. In any setof eight hexagonal gluing diagrams, why must there always be such a pair? Demonstratethat your pair represents the same surface, by modifying the diagrams until they agree.

First Exam AB


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First Exam AC


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First Exam AD


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First Exam BA


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First Exam BC


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First Exam BE


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First Exam BG


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First Exam BK


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First Exam BL


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First Exam BM


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First Exam BN


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First Exam CA


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First Exam CD


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First Exam CE


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First Exam CF


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First Exam CG


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First Exam CH


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First Exam CI


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First Exam CJ


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First Exam CK


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First Exam CL


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First Exam CM


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First Exam DA


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First Exam DB


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First Exam DC


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First Exam DG


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First Exam DH


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First Exam DJ


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First Exam DK


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First Exam DL


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First Exam DM


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First Exam DN


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First Exam ED


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First Exam EF


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First Exam EG


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First Exam EI


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First Exam EK


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First Exam EL


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First Exam EM


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First Exam EN


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First Exam FG


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First Exam FK


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First Exam FN


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First Exam GC


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First Exam GD


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First Exam GE


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First Exam GG


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First Exam GK


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First Exam GL


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First Exam GN


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First Exam HA


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First Exam HB


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First Exam HC


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First Exam HD


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First Exam HE


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First Exam HF


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First Exam HG


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First Exam HH


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First Exam HI


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First Exam HJ


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First Exam HK


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First Exam HL


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First Exam HM


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First Exam HN


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First Exam IA


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First Exam IB


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First Exam IC


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First Exam ID


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First Exam IE


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First Exam IF


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First Exam IG


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First Exam IH


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First Exam II


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First Exam IJ


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First Exam IK


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First Exam IL


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First Exam IM


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First Exam IN


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First Exam JA


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First Exam JB


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First Exam JC


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First Exam JD


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First Exam JE


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First Exam JF


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First Exam JG


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First Exam JH


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First Exam JI


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First Exam JJ


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First Exam JK


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First Exam JL


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First Exam JM


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First Exam JN


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First Exam KA


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First Exam KB


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First Exam KC


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First Exam KD


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First Exam KE


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First Exam KF


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First Exam KG


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First Exam KH


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First Exam KI


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First Exam KJ


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First Exam KK


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First Exam KL


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First Exam KM


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First Exam KN


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First Exam LA


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First Exam LB


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First Exam LC


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First Exam LD


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First Exam LE


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First Exam LF


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First Exam LG


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First Exam LH


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First Exam LI


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First Exam LJ


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First Exam LK


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First Exam LL


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First Exam LM


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First Exam LN


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First Exam MA


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First Exam MB


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First Exam MC


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First Exam MD


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First Exam ME


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First Exam MF


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First Exam MG


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First Exam MH


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First Exam MI


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First Exam MJ


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First Exam MK


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First Exam ML


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First Exam AA - Columbia Universitybayer/S02/knots/midterm1.pdfFirst Exam AA Surfaces and Knots,...

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