Timeline for Homology dimension of the mapping class group of a surface with boundary
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2010 at 10:50 | comment | added | HYYY | Hi,Oscar,thank you for your help. but could you show me why that is a sphere bundle assoicated to the tangent bundle? and is that fibration just a fiber bundle?Thanks! | |
| Jul 30, 2010 at 15:09 | comment | added | Oscar Randal-Williams | If you take reduced homology this problem does not appear. | |
| Jul 30, 2010 at 13:10 | vote | accept | HYYY | ||
| Jul 30, 2010 at 13:10 | comment | added | HYYY | Hi,Oscar, according to your argument, it seems that I can show the homology of $M^{b,m}_{g,n}$ (here, there could be marked points on the boundary,for which $m=(m_1,m_2,\ldots,m_b), m_i$ is the number of marked points on the $i$th boundary component) vanishes in degrees at least $6g-7+2n+3b+m$. However, when $6g-7+2n+3b+m=0$,$H_0$ will not be 0. Is this result true for other cases except the cases for $6g-7+2n+3b+m=0$? In fact, for the homology dimension for closed surface we need to exclude the case $(g,n)=(0,3)$ because $H_0$ is also not 0. How to deal with such things? Thanks! | |
| Jul 30, 2010 at 7:55 | history | answered | Oscar Randal-Williams | CC BY-SA 2.5 |