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Dec
18
comment proof that $PSL(2,\mathbb{R})$ is $SO^+(2,1)$
Related: math.stackexchange.com/q/491455 (a map from SO(1,3) to PSL(2,C) etc)
Dec
18
comment Functors that are the homology of a chain complex
@ZhenLin $K(A,n)$ can be defined as $B^nA$ (or using Dold–Puppe). In this construction it's a topological abelian group, so $[X,K(A,n)]$ clearly is an abelian group. Now the question is why this homological functor can be lifted to a triangulated functor to $D(Ab)$, something like this.
Dec
18
comment Proving that $\left(\frac{\pi}{2}\right)^{2}=1+\sum_{k=1}^{\infty}\frac{(2k-1)\zeta(2k)}{2^{2k-1}}$.
Interesting. But why first equality holds?
Dec
18
comment Quaternion Projective Space
Related: What is the Cayley projective plane?
Dec
18
comment Conditions for a Topological space to be a Spectrum
Being spectrum is an extra structure, not just a condition (i.e. one should fix all deloopings)
Dec
15
comment Limit of $\sum_{i=1}^n \left(\frac{{n \choose i}}{2^{in}}\sum_{j=0}^i {i \choose j}^{n+1}\right)$
Have you tried using Stirling's approximation?..
Dec
15
comment Linear structure on the category of formal groups
You're talking about 1-dimensional FG, right? Because in general FG over R is not isomorphic to additive FG.
Dec
13
comment Moves for regular homotopies of immersions of $S^1$ in the plane
AFAIR two such immersions are equivalent iff they have the same winding number (H. Whitney. On regular closed curves in the plane), no?
Dec
13
comment CW-complex with zero boundary operators
Cf. definition of formal dg-algebra, btw
Dec
13
comment CW-complex with zero boundary operators
Homology groups are not always free, you know...
Dec
13
comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
Related: How does one motivate the analytic continuation of the Riemann zeta function?
Dec
13
comment Different methods to prove $\zeta(s)=2^s\pi^{s-1}\sin\left(\frac{s\pi}{2}\right) \Gamma (1-s) \zeta (1-s)$.
Related: Riemann's thinking on symmetrizing the zeta functional equation
Dec
11
comment Binomial Identity $\sum\binom{2n+1}{2k+1}\binom{m+k}{2n} = \binom{2m}{2n}$
Interesting. RHS is of course a coefficient of $(1+t)^{2m}$ and LHS looks almost like trinomial expansion...
Dec
11
comment Line bundles over $\mathbb R P^2$
Hint: $\mathbb RP^2$ can be covered by 3 affine charts (on each of which the bundle is trivial)
Dec
10
comment Are spaces with isomorphic fundamental groups homotopically equivalent?
Related: math.stackexchange.com/q/1901
Dec
10
comment Hopf fibration and $\pi_3(\mathbb{S}^2)$
Related: maths.ed.ac.uk/~aar/papers/samelson.pdf
Dec
9
comment Proving $\sum_{k=0}^{2m}(-1)^k{\binom{2m}{k}}^3=(-1)^m\binom{2m}{m}\binom{3m}{m}$ (Dixon's identity)
Related: Combinatorial Proof of Dixon's Identity
Dec
9
comment Geometric interpretation of the cofactor expansion theorem
Yes, $(u,v)$ is the scalar product. $e_i$ is the basis of our space (in which all vectors lie; $e_2=(0,1,0,...)$ and so on, if you will).
Dec
7
comment Geometric interpretation of the cofactor expansion theorem
Ah, so you work in the Clifford algebra essentially, I see.
Dec
7
comment Geometric interpretation of the cofactor expansion theorem
@dfg I've tried to give two different proofs of this fact — one in 2. (check it for basis vectors and use linearity) and one in 3. (choose a basis such that statement becomes obvious). The main ingredient is the observation that, say, $A_{11}$ is the area of the projection of the base on the hyperplane «first coordinate is zero».