18h
comment knotted Riemann surfaces
A 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 Bundles
Yes, 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 tangent
edited 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 Manifolds
There'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
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