Recent content by polology

Thank for your answer. About the first question, I figured it out. I've had just a bit of confusion about the vector field, since I know that its components are functions, but I used to see it as a functional rather than a function, but I forgot the trivial thing that the functional is itself a...

Following Steinacker's book we can say that given the manifold ##N## of a configuration space and its tangent bundle ##TN## we define a differentiable function ##L(\gamma,\dot\gamma): TN\rightarrow \mathbb{R}## and call it the Lagrangian function. We know there's always an isomorphism between a...

Thank you again for your answers and patience, the exam went well :)

Okay, here I am. Sincerely it was hard for me to have a deep understanding of some things of the previous answers due to my unfamiliarity with these concepts (i think after the exam i'll come back here to have a better understanding), but the last answer was extremely helpful. I'll try to give a...

Hi @mathwonk thank you a lot for those answers! It's been a while since I was searching for someone who could help me understand those concepts. I can't answer you in the conversation you opened because for unknown reasons the site detects some spam-like content in my reply. Sorry if I haven't...

Thank you very much! here it is: and this is the paper: https://arxiv.org/abs/1402.3140 I have some questions because I'm new to many of these concepts. In polyhedral decomposition I do a triangulation of the manifold and associate a cycle to every open set, and I can obtain the boundaries...

I'm studying Chern-Simons theory on topological nontrivial 3-manifold (I come from a physics background, so I'm new to some mathematical concepts). If the first homology group $H_1(M)$ is nontrivial one needs to consider a good cover of the manifold and a polyhedral decomposition. Then, we can...