bio | website | |
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location | ||
age | ||
visits | member for | 3 years, 6 months |
seen | yesterday | |
stats | profile views | 3,249 |
Taking a break for a while.
Aug
13 |
awarded | Self-Learner |
Aug
11 |
comment |
Version of Stone Weierstrass for functions not vanishing at infinity
Crossposted on MSE. |
Aug
11 |
comment |
What is an intuitive explanation of the Hopf fibration and the twisted Hopf fibration?
Crossposted on MSE. |
Aug
6 |
comment |
Stokes-like Theorem for Dolbeault Operator
I should have pointed this out before, if $\theta = dz_1\wedge\dots\wedge dz_n$, then $\theta$ is a $(n, 0)$-form, not a $(0, n)$-form. What is the volume form you are using to integrate the function you extract? |
Aug
6 |
comment |
Stokes-like Theorem for Dolbeault Operator
I'm not sure what can be said. First of all, it's not clear to me why you would call a $(0, n)$-form a volume form. Second of all, you can only integrate an $n$-form on an real $n$-dimensional manifold. If $n = 1$, $M$ is a compact Riemann surface. In this scenario, what would you integrate a $(0, 1)$-form over? |
Aug
6 |
answered | Stokes-like Theorem for Dolbeault Operator |
Jul
28 |
answered | Examples of common false beliefs in mathematics |
Jul
26 |
comment |
Is there a generalization of homotopy groups to fractional dimensions
Is there a pointed topological space $S^{\frac{1}{2}}$ such that $S^{\frac{1}{2}}\wedge S^{\frac{1}{2}} = S^1$? |
Jul
23 |
reviewed | No Action Needed Some references for f-ring |
Jul
22 |
comment |
Can view the connected component of the Picard scheme $\text{Pic}^0(X)$ as a “kernel” of the first Chern class?
Not sure how helpful this is (I'm not an algebraic geometer), but I thought I would mention it. In Huybrechts' Complex Geometry: An Introduction, the Jacobian of a complex manifold $X$, denoted $\operatorname{Pic}^0(X)$, is defined as the kernel of the map $c_1 : \operatorname{Pic}(X) \to H^2(X, \mathbb{Z})$. Using the exponential sequence, one can show that $\operatorname{Pic}^0(X) \cong H^1(X, \mathcal{O})/H^1(X, \mathbb{Z})$. |
Jul
19 |
awarded | Marshal |
Jul
18 |
comment |
Dimension of two homotopy equivalent manifolds
Isn't $H_2(\mathbb{RP}^2, \mathbb{Z}) = 0$? |
Jul
15 |
comment |
Chern classes, vanishing of smooth sections or vanishing of holomorphic?
I believe you mean smooth sections rather than dual sections. |
Jul
15 |
reviewed | No Action Needed How to characterize flasque sheaves in more functorial way? |
Jul
14 |
reviewed | No Action Needed Example of a pair which is not weakly annihilating |
Jul
14 |
comment |
Question on product measure
Crossposted on MSE. |
Jul
13 |
revised |
Why is the fundamental group of a compact Riemann surface not free ?
Fixed the spacing of the matrices by changing \\\\ to \\. |
Jul
13 |
suggested | approved edit on Why is the fundamental group of a compact Riemann surface not free ? |
Jul
13 |
reviewed | No Action Needed The Matrix-Tree Theorem without the matrix |
Jul
8 |
revised |
Exotic group topologies on the affine group $ax+b$
Added MathJax and a tag. |