Reputation
11,615
Next tag badge:
365/400 score
65/80 answers
Badges
3 41 87
Impact
~167k people reached

Jan
4
comment Special Cases of Quadratic Reciprocity and Counting Fixed Points
Nice indeed! But it's not immediately clear how to generalize this: it's easy to find 3-torsion in $PSL_2(\mathbb Z)\cong\mathbb Z_2\ast\mathbb Z_3$ but not, say, 5-torsion...
Jan
3
comment A combinatorial identity: $ \sum_{k=m}^n \frac{\binom{1/2}{k-m}}{k \binom{-1/2}{k}}=\frac{\binom{-1/2}{n-m}}{m \binom{-1/2}{n}} $
Looks amusing. What's the source?
Jan
3
comment Show $\binom{n}{k}\binom{k}{a} = \binom{n}{a}\binom{n-a}{k-a}$ by block-walking interpretation of Pascal's triangle
Related: math.stackexchange.com/q/534202
Jan
3
comment Is there anything to be learned from the spectrum of a cohomology ring?
AFAIK this POV is more useful in equivariant cohomology. For example, in the context of localization theorems it's natural (at least) to view $H_G(X)$ as a sheaf over $\operatorname{Spec}H_G(pt)$. See also Quillen. The Spectrum of an Equivariant Cohomology Ring and Goresky, MacPherson. On the Spectrum of the Equivariant Cohomology Ring...
Jan
3
comment Loop space and $K$-theory
possible duplicate of Yoneda's lemma and $K$-theory.
Jan
2
comment Understanding the relationship between $Sp(n)$ and $Sp(2n,\mathbb{C})$
Have you tried Wikipedia?
Jan
2
comment Explicit formula for Fermat's 4k+1 theorem
Shouldn’t this ‘Weyl’ be ‘Weil’?
Jan
2
comment Can the equivalence between principle bundles and maps to classifying spaces be turned into an adjunction.
I'm not sure I understand your question. You want adjunction between what what and what? If you're talking about categories $Bun_G(X)$ and $[X,BG]$ — sure, any equivalence of categories can be refined to an adjoint equivalence.
Jan
2
comment Prove that $\sum_{k=0}^{m}\binom{m}{k}\binom{n+k}{m}=\sum_{k=0}^{m}\binom{n}{k}\binom{m}{k}2^k$
(Cf. [shifted] Legendre polynomials, btw!)
Jan
2
comment The importance of generating series
I don't think this has anything to do with algebraic geometry. Generating functions is a useful machine to work with any large collection of numbers satisfying some recurrence relation(s).
Jan
1
comment Semialgebraic conditions that convey properties of Galois group
The word is semi-algebraic (if I understand OP correctly)
Jan
1
comment Proof of $0! = 1$
Basically, this is just a convention. But notice how nicely this agrees with general formula $n!=n\cdot(n-1)!$ (take $n=1$).
Dec
31
comment Contracting a contractible set in $\mathbb R^2$
Moore's theorem is that for a closed equivalence relation on the 2-sphere such that all equivalence classes are connected and non-separating, and not all points are equivalent, the quotient space is homeomorphic to the 2-sphere, I guess?
Dec
31
comment Contracting a contractible set in $\mathbb R^2$
@M314 Complement to the horned ball is not simply connected. So in $\mathbb R^3/A$ we have a point $A/A$ with non-simply-connected complement.
Dec
30
comment Mapping cylinder is a CW complex
Have you seen section 'Topology of Cell Complexes' in Hatcher? At least product of CW-complexes is discussed in detail there.
Dec
30
comment Cohomology Ring of Projective Space
Related: Proving that the cohomology ring of $\mathbb{R}P^n$ is isomorphic to...
Dec
30
comment Cohomology ring of $\mathbb R P^\infty$ with $\mathbb Z_{2k}$ coefficients
Related: the same question for $k=2$
Dec
30
comment Contracting a contractible set in $\mathbb R^2$
I'm not even sure if this is true — for example for $\mathbb R^3$ the statement seems to be false (take $A$ to be the horned ball...).
Dec
29
comment Contracting a contractible set in $\mathbb R^2$
$S^1\subset\mathbb R^2$ is compact and connected but not contractible.
Dec
29
comment Concrete non trivial computation of Morse homology
[Let's wait for answers but] I've always thought it's mainly useful for (co)homology of loop space and such [and not in finite-dimensional situation]...