# Tagged Questions

**0**

votes

**1**answer

134 views

### from Dehn twists to surgery diagram [closed]

Assume the relation $(ab)^6=1$, for $a$ and $b$ Dehn twists about the meridian and the longitude of a torus. Now if we glue the two ends of $T\times I$ together by either the diffeomorphism $(ab)^6$ ...

**6**

votes

**1**answer

125 views

### What is the order of the isotopy group of the Brieskorn homology 3-sphere?

Let $\Sigma(p,q,r)$ be the Brieskorn homology 3-sphere with $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}<1$ (so not the 3-sphere or the Poincare sphere). The fundamental group is given by $$ ...

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**1**answer

189 views

### mapping class group of a surface

I want to know what techniques are known to present a diffeomorphism on a surface with boundary (the diffeomorphism is not necessarily the identity restricted to the boundary) as product of Dehn ...

**8**

votes

**1**answer

184 views

### Isotopy classes on the disk and mapping tori

Is the following true?
"The conjugacy classes of two homeomorphisms of the n-times punctured disk have isotopic representatives iff the associated mapping tori are homeomorphic."
By conjugacy class ...

**0**

votes

**1**answer

336 views

### pseudo-Anosov maps on surfaces with boundary

In "Automorphisms of Surfaces after Nielsen & Thurston" by Casson & Bleiler (on pages 75 - 80) they discuss classifying automorphisms of a surface. They show that, if $S$ is a closed ...

**13**

votes

**2**answers

451 views

### The kernel of the map from the handlebody group to Outer automorphisms of a free group

Let $K$ be a compact oriented 3-dimensional handlebody of genus $g$. The group $H_g$ of isotopy classes of diffeomorphisms of $K$ is called the handlebody group. (It embeds as a subgroup of the ...

**2**

votes

**3**answers

564 views

### Reducible 3d torus bundles

Here reducible means that the mapping class for the fiber is a reducible auto-homeomorph in the sense of Nielsen-Thruston. So,
could anyone give me a hint to classify them?
In contrast, do you agree ...