Timeline for Mapping-Class Groups of Subsurfaces of a Hyperbolic Surface
Current License: CC BY-SA 3.0
3 events
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| Nov 15, 2017 at 7:19 | comment | added | HJRW | @QGravity, it sounds like you're interested in the case when every puncture of $\mathcal{R}''$ is a puncture of $\mathcal{R}$. In this case, the homomorphism is injective, for the simple reason that any homotopy can be extended across the boundary by the identity. | |
| Oct 16, 2017 at 2:38 | comment | added | QGravity | Thank you for the answer. The case where the subsurface is closed is treated on page 83 of a primer on mapping-class group and the condition for injectivity is given. However, I am most interested in the case that the subsurface $\mathcal{R}''$ can be obtained by removing a number of pair of pants from the original surface $\mathcal{R}$. If $\mathcal{R}$ is a punctured surface, then by removing one or more pair(s) of pants we are left with a surface with boundaries and punctures. I am most interested in this case. | |
| Oct 16, 2017 at 2:25 | history | answered | Igor Rivin | CC BY-SA 3.0 |