# Tag Info

Accepted

### Which mapping class group representations come from algebraic geometry?

Dan, Although I'm no longer very active on MO, I thought I'd make a few comments, since your question is an interesting one (and you're not anonymous). The paper of Looijenga referenced in Igor's ...
• 31.7k

### Mapping Class Group (MCG) of connected sum of 3-torus and $S^2\times S^1$

The mapping class groups of all compact orientable 3-manifolds are essentially known. A fairly detailed summary of the results, focusing on the nonprime case and with references to proofs in the ...
• 18.6k
Accepted

### Conjugacy classes of the mapping class group

An exponential-time solution to the conjugacy problem in the mapping class group was given by Jing Tao, in: Tao, Jing(1-OK) Linearly bounded conjugator property for mapping class groups. (English ...
• 22.3k
Accepted

• 3,055

• 39.8k

### Is there a Morita cocycle for the mapping class group Mod(g,n) when n > 1?

The answer is "yes" -- in fact one can do better and get a class in $$H^1(\text{Aut}(F_m), \text{Hom}(H, \wedge^2 H)),$$ where $F_m$ is the free group on $m$ generators and $H$ is the ...
• 20.5k
Accepted

### Minimal number of (Dehn twists) generators of the mapping class group of a marked sphere

The minimum number of Dehn twist generators (and in fact the minimum number of generators of any kind) for $\Gamma_{0,n}$ is ${n-1 \choose 2} - 1$. Here's why. A presentation for $\Gamma_{0,n}$ is ...
• 141

### $\mathbb{R}P^n$ bundles over the circle

No. Every smooth bundle over $S^1$ with fiber $M$ is the mapping torus of some diffeomorphism $f:M\to M$. Isomorphism classes of bundles correspond to conjugacy classes in the group of isotopy classes ...
• 47.5k

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