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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.