Search results

...(A)+\frac13 \int_\mathbb{R^3}Tr(g^{-1} d g \wedge g^{-1} d g \wedge g^{-1} d g)$ $$CS(A^g)=\int_\mathbb{R^3} Tr(A^g \wedge d A^g + \frac23 A^g \wedge A^g \wedge A^g)$$

...= A\wedge \mathrm{d}A</math> is invariant under <math>A\mapsto A + \mathrm{d}f</math>''' \Psi(A + \mathrm{d}f) &= (A + \mathrm{d}f)\wedge \mathrm{d}(A + \mathrm{d}f)\\

More on pushforwards, <math>d^{-1}</math>, and <math>d^\ast</math>.

$$d(gs) = (dg)s+gds \implies (dg)s = d(gs)-gds$$ D_{g^{-1} A g+g^{-1} d g} (s)\\

A^{(gh)} &= (gh)^{-1}A(gh) + (gh)^{-1}\mathrm{d}(gh) \\ &= (gh)^{-1}A(gh) + (gh)^{-1}\Big((\mathrm{d}g)h + g(\mathrm{d}h)\Big)\\

...to produce a <math>k+1</math>-form and that <math>\mathrm{d}\circ \mathrm{d} =0</math>. ...rm so that <math>\mathrm{d}f \in \Omega^1(M)</math>. Thus <math>d: \mathrm{d} \Omega^0(\mathbb{R}^3) \rightarrow \Omega^1(\mathbb{R}^3)</math> is the gr

Fourth red relation on the right should be <math>D=\partial(d)A^{-1}GA</math>

...in D}(\Phi_{\vec{e}}^\ast\omega_3)_{21}\prod_{\text{black}\atop \vec{e}\in D}(\Phi_{\vec{e}}^\ast\omega_1)_{10}</math>. I'll try to explain and make a p

Some analysis of <math>d^{-1}</math>.

The correct definition of <math>d^*</math>.

A Drinfel'd-Kohno theorem.

A naive way to define <math>d^*</math>.

...a metric space. Prove that the metric itself, regarded as a function <math>d\colon X\times X\to{\mathbb R}</math>, is continuous. ...(x,A):=\inf_{y\in A}d(x,y)</math>, is a continuous function and that <math>d(x,A)=0</math> iff <math>x\in\bar{A}</math>.

The dual of <math>H^0(\mathcal{D}_n)</math>.

...um of all $\mathcal{D}^{pb}_m$, and define $\mathcal{A}^{pb}$ as $\mathcal{D}^{pb}/\mathcal{I}$, where $\mathcal{I}$ is an ideal generated by relations

I have noticed that the d<math>x</math> always comes before the integrand. Any reason for this or it

...ac{\partial L}{\partial q}\delta q+\frac{\partial L}{\partial\dot{q}}\frac{d}{dt}\left(\delta q\right)\right).</math> ...|_{t_i}^{t_f}=\int_{t_i}^{t_f}dt \left(\frac{\partial L}{\partial q}-\frac{d}{dt}\left(\frac{\partial L}{\partial\dot{q}}\right)\right)\delta q,</math>

...w becomes a single variable minimum/maximum problem. We set <math>\frac{d}{d\epsilon}f(\epsilon)\mid_{\epsilon=0} = 0</math>, and solve for <math>x_c</m <math>\frac{d}{d\epsilon}f(\epsilon)\mid_{\epsilon=0} = \int_0^T dt(\dot{x}_c\dot{x}_q - x_q

...a metric space. Prove that the metric itself, regarded as a function <math>d\colon X\times X\to{\mathbb R}</math>, is continuous. ...(x,A):=\inf_{y\in A}d(x,y)</math>, is a continuous function and that <math>d(x,A)=0</math> iff <math>x\in\bar{A}</math>.

...Johnson homomorphism. In the Artin case, this is the action of the Drinfel'd-Kohno Lie algebra on the free Lie algebra.