Zobrazeno 1 - 10
of 45
pro vyhledávání: '"55P62 (primary)"'
Autor:
Sati, Hisham, Voronov, Alexander A.
In previous work, we introduced Mysterious Triality, extending the Mysterious Duality of Iqbal, Neitzke, and Vafa between physics and algebraic geometry to include algebraic topology in the form of rational homotopy theory. Starting with the rational
Externí odkaz:
http://arxiv.org/abs/2408.13337
Autor:
Voronov, Alexander A.
This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership.
Comment: 19 pages, submitted as a chapter in Encyclopedia of Mathematical Physics, 2nd edition
Comment: 19 pages, submitted as a chapter in Encyclopedia of Mathematical Physics, 2nd edition
Externí odkaz:
http://arxiv.org/abs/2404.00939
We give an explicit minimal Quillen model for the Cartesian product $X\times Y$ of rational $2$-cones in terms of derivations and a binary operation $\star \colon \mathbb{M}(V)\otimes \mathbb{L}(W)\to \mathbb{L}(V\oplus W\oplus s(V\otimes W))$, where
Externí odkaz:
http://arxiv.org/abs/2402.18168
Autor:
Berglund, Alexander, Stoll, Robin
These notes are based on a series of three lectures given (online) by the first named author at the workshop "Higher Structures and Operadic Calculus" at CRM Barcelona in June 2021. The aim is to give a concise introduction to rational homotopy theor
Externí odkaz:
http://arxiv.org/abs/2310.11824
Autor:
Berglund, Alexander, Zeman, Tomáš
We prove new structural results for the rational homotopy type of the classifying space $B\operatorname{aut}(X)$ of fibrations with fiber a simply connected finite CW-complex $X$. We first study nilpotent covers of $B\operatorname{aut}(X)$ and show t
Externí odkaz:
http://arxiv.org/abs/2203.02462
Autor:
Zoller, Leopold
Let $T$ be a compact torus. We prove that, up to equivariant rational equivalence, the category of $T$-simply connected, $T$-finite type $T$-spaces with finitely many isotropy types is completely described by certain finite systems of commutative dif
Externí odkaz:
http://arxiv.org/abs/2106.00363
Autor:
Kennard, Lee, Wu, Yantao
A 1976 conjecture of Halperin on positively elliptic spaces was recently confirmed in formal dimensions up to 16. In this article, we shorten the proof and extend the result up to formal dimension 20. We work with Meier's algebraic characterization o
Externí odkaz:
http://arxiv.org/abs/2104.04086
Autor:
Amann, Manuel
The toral rank conjecture speculates that the sum of the Betti numbers of a compact manifold admitting a free action of a torus of rank $r$ is bounded from below by $2^r$. Clearly, such an action yields a torus bundle, and, more generally, the same c
Externí odkaz:
http://arxiv.org/abs/2011.13411
In this paper, we show that for finite $CW$-complexes $X$ and two-stage space $Y$ (for example $n$-spheres $S^n$, homogeneous spaces and $F_0$-spaces), the rational homotopy type of $\map(X, Y)$ is determined by the cohomology algebra $H^*(X; \Q)$ an
Externí odkaz:
http://arxiv.org/abs/2010.04579
Autor:
Amann, Manuel
Motivated by prominent problems like the Hilali conjecture Yamaguchi--Yokura recently proposed certain estimates on the relations of the dimensions of rational homotopy and rational cohomology groups of fibre, base and total spaces in a fibration of
Externí odkaz:
http://arxiv.org/abs/2006.03390