# Tagged Questions

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### isotopy classes of embeddings of the torus

Let's consider $S^1$-bundle $E$ over a 2-manifold $M$. How many isotopy classes of embeddings of the torus $\mathbb{T}^2$ in $E$?
For each free homotopy classes $\gamma$ of mappings of the circle ...

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### Second Homotopy Group of Graph Manifolds

A graph manifold is a closed 3-manifold $M$ that admits a finite collection of disjoint embedded tori $\mathcal{T}$ so that $M \setminus \mathcal{T}$ is a disjoint union of Seifert fibred spaces (i.e. ...

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### Does a homeomorphism of $S^1 \times S^2$ which is homotopy to the identity has to isotope to it?

I guess the question can be asked for all manifolds. But I am particularly interested in $S^1 \times S^2$ right now. Concrete example preferrd.

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### Intutive interpretation about Linking forms

Let $M^3$ be a rational homology 3-sphere. (i,e, $M^3$ is closed 3-manifold with
$H_{*}(M;Q)=H_{*}(S^3;Q)$
As beautifully explained in Ranicki's Algebraic and Geometry surgery book and Davis-Kirk's ...