## Question

###### 5 marks) Let S be a closed orientable surface, and let P be some point on the surface $ Suppose you have two paths a and B in S such that:both a and 8 start and end at P- does not cross itself anywhere, and neither does 8; a and 8 do not meet anywhere except the start /end point P the intersection of & and 8 at point P is tranverse, not tangential (see the diagram below)TransvecseTangentialProve that the surface S must be of the form Torus # U for some closed surface U

5 marks) Let S be a closed orientable surface, and let P be some point on the surface $ Suppose you have two paths a and B in S such that: both a and 8 start and end at P- does not cross itself anywhere, and neither does 8; a and 8 do not meet anywhere except the start /end point P the intersection of & and 8 at point P is tranverse, not tangential (see the diagram below) Transvecse Tangential Prove that the surface S must be of the form Torus # U for some closed surface U

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