Hi Again:(adsbygoogle = window.adsbygoogle || []).push({});

Let S_2, be the genus-2 connected, orientable surface, i.e.,

the connected sum of 2 tori (e.g., tori spelling and some other tori)

Consider a pair {C1,C2} of homologous, non-trivial curves, i.e.,

neither C1 nor C2 bounds, but C1-C2 is a (sub)surface in S_2.

Consider now a pair {D1,D2) of Dehn twists about each of C1,C2 ,

but in opposite directions; these Dehn twists about curves like

{C1,C2} are called bounding pairs. Still, for genus g=2, these

maps are trivial. Why is this so?

We clearly have only two classes of nonbounding curves , but I don't see

why , nor in what sense this map is trivial.

Any Ideas?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Bounding Pairs of Dehn Twists are Trivial

**Physics Forums | Science Articles, Homework Help, Discussion**