First Exam AA - Columbia Universitybayer/S02/knots/midterm1.pdfFirst Exam AA Surfaces and Knots, Dave Bayer, February 21, 2002 Name: School: [1] [2] [3] [4] [5] TOTAL Youmay use scratch

First Exam AA

Surfaces and Knots, Dave Bayer, February 21, 2002

Name: School:

[1] [2] [3] [4] [5] TOTAL

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


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam AN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam BN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam CN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam DN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam ED


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam EN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam FN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam GN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam HN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam ID


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam II


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam IN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam JN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam KN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LE


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LL


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LM


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam LN


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MA


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MB


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MC


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MD


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam ME


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MF


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MG


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MH


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MI


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MJ


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam MK


Name: School:

[1] [2] [3] [4] [5] TOTAL







First Exam ML


Name: School:

[1] [2] [3] [4] [5] TOTAL







Documents

First Exam AA - Columbia Universitybayer/S02/knots/midterm1.pdfFirst Exam AA Surfaces and Knots, Dave Bayer, February 21, 2002 Name: School: [1] [2] [3] [4] [5] TOTAL Youmay use scratch