# Henry T. Horton

 18h comment knotted Riemann surfacesA knot is more than just a copy of $S^1$, it is an embedding of $S^1$ in $S^3$. To know if a Riemann surface is "knotted" you can't just consider it as a complex curve, it needs to be embedded somewhere. After you embed it somewhere you need to decide what it means for the embedding of a Riemann surface to be knotted. Apr 18 revised Why is $[\widetilde{v},\widetilde{w}]_p(f)=0$ when $f$ has a critical point at $p$?added 489 characters in body Apr 18 answered Why is $[\widetilde{v},\widetilde{w}]_p(f)=0$ when $f$ has a critical point at $p$? Apr 1 answered Connection on canonical $\operatorname{Spin}^\mathbb{C}$ spinor bundle on symplectic manifold Mar 26 answered Understanding $r:\mathfrak{g}\rightarrow Vect(X)$ is the transpose of $d\mu:TX\rightarrow \mathfrak{g}^*$ Mar 25 answered Universal Equivariant Line Bundles Mar 24 comment Universal Equivariant Line BundlesYes, and the construction is similar to the nonequivariant case. Let $V$ be the direct sum of countably many copies of each irreducible complex representation of $G$, let $BU_G$ be the space of $1$-dimensional subspaces of $V$, and let $EU_G$ be the space of pairs $(\ell, v)$ where $\ell \in BU_G$ and $v \in \ell$. Then $\pi: EU_G \to BU_G$, $\pi(\ell, v) = \ell$ is a universal $G$-equivariant line bundle. Mar 20 awarded Enlightened Mar 20 awarded Nice Answer Mar 2 comment Notations in Riemannian Geometry$i^\ast TN$ denotes the pullback of the bundle $TN$ via the map $i$: en.wikipedia.org/wiki/Pullback_bundle. It has a different meaning than the map $i^\ast : T^\ast N \longrightarrow T^\ast M$ and in particular does not mean the image of $TN$ under the map $i^\ast: T^\ast N \longrightarrow T^\ast M$ (which does not make sense). Feb 24 answered Bakry-Emery Laplacian and Hodge Decomposition Feb 13 awarded Yearling Feb 13 awarded Yearling Feb 13 awarded Yearling Feb 13 awarded Yearling Feb 7 revised Find the equation of two straight lines tangentedited tags Feb 2 reviewed Reject suggested edit on Ways to put $5$ balls in $3$ boxes if each box must contain at least $1$ ball. Jan 31 comment Involutive Properties of Space-structures on Smooth ManifoldsThere's nothing particularly wrong with Turaev's book. You can read the original Reshetikhin-Turaev papers to see their construction of a 3-manifold invariant. The papers are very readable, especially if you have already been going through Turaev's book. Another reference is Kock's book, but it only treats the case of 2D TQFTs. Kock's book is very easy to read, however, and will give you a good idea of what TQFT is about. Jan 31 reviewed Reject suggested edit on Differential Equations: Separable Equations Jan 31 answered Involutive Properties of Space-structures on Smooth Manifolds