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Mathoverflow.net news digest

  • 0 days

    Is the set theoretic multiverse view akin to the idea in proof theory that diffe...

    In formal logic and proof theory we often study different axiomatic systems for the sake of it. It is considered interesting to see what theorems and derivations one can prove. One can attempt to ascribe certain kinds of meanings to the symbols, too...

  • 14 years

    A product approximation to the Taylor series of the exponential

    I recently came across the following in something I'm working on, and I'd never seen it before. Consider\begin{align*}f_1(x) &= (1+x)^{1/1} \\\f_2(x) &= (1+x)^{2/1} (1+2x)^{-1/2} \\\f_3(x) &= (1+x)^{3/1} (1+2x)^{-3/2} (1+3x)^{1/3} \\\f_4...

  • 15 years

    third stable homotopy group of spheres via geometry?

    It is ''well-known'' that the third stable homotopy group of spheres is cyclic of order $24$. It is also ''well-known'' that the quaternionic Hopf map $\nu:S^7 \to S^4$, an $S^3$-bundle, suspends to a generator of $\pi_8 (S^5)=\pi_{3}^{st}$. It is even...

  • 0 days

    Nice exact unitary matrices for the faithful 6 dimensional representation of $6....

    Cross-posted to MSE where it received 2 upvotes but no answers.
    I am looking for a reasonably nice exact unitary model of the faithful 6-dimensional complex representation of the Schur cover $6.A_7$.
    The ATLAS gives characteristic-zero generators for the representation labeled something like$$6.A_7,\qquad 6(a),\qquad \dim=6,$$over a small algebraic field, essentially$$K=\mathbb Q(\sqrt{2},\zeta_3).$$...

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