Timeline for Mapping Class Group (MCG) of connected sum of 3-torus and $S^2\times S^1$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2016 at 9:34 | comment | added | SKShukla | Thank you very much for such a detailed reply. It has been very helpful! Being in physics, I work with the triangulated manifolds (lets say a $\Delta$-complex). For example, $MCG(T^n)$ action on triangulated n-torus is widely used in physics. But when I tried to represent Dehn Twisting sphere as action on a complex, I run into problems. Does the essence of MCG described above remain the same going to triangulated manifolds, or does it change nontrivially? I see a paper by you on MCG action on 2D- complex. I cannot find one on 3D- complex though. Thank you. | |
| Jul 30, 2016 at 19:41 | history | edited | Allen Hatcher | CC BY-SA 3.0 |
Gave more details.
|
| Jul 30, 2016 at 2:55 | comment | added | SKShukla | Thank you very much for your answer! I am reading your paper and indeed it's clarifying a lot of things. However, I am new to the subject (and I am a physicist) so I still need to learn a few things. I think I understand the points regarding $ker(\Phi)$ and $imag(\Phi)$ but I am having trouble picturing geometrically what $\Phi$ itself is for elements outside $ker(\Phi)$. In 2D, MPG is generated by Dehn twist along different loops in the fundamental group. What kind of twisting is typically involved in 3D? thanks! | |
| Jul 29, 2016 at 13:35 | history | answered | Allen Hatcher | CC BY-SA 3.0 |