Zobrazeno 1 - 10
of 52
pro vyhledávání: '"WIERSTRA, FELIX"'
Topological Data Analysis (TDA) is increasingly crucial in investigating the shape of complex data structures across scientific fields, particularly in neuroscience and finance. This study delves into persistent homology, a TDA component initially ai
Externí odkaz:
http://arxiv.org/abs/2311.17912
Autor:
de Kleijn, Niek, Wierstra, Felix
The Deligne-Getzler-Hinich--$\infty$-groupoid or Maurer-Cartan simplicial set of an $L_\infty$-algebra plays an important role in deformation theory and many other areas of mathematics. Unfortunately, this construction only works over a field of char
Externí odkaz:
http://arxiv.org/abs/2303.16706
Over a field of characteristic zero, we show that the forgetful functor from the homotopy category of commutative dg algebras to the homotopy category of dg associative algebras is faithful. In fact, the induced map of derived mapping spaces gives an
Externí odkaz:
http://arxiv.org/abs/2211.02387
Our main result is a recognition principle for iterated suspensions as coalgebras over the little disks operads. Given a topological operad, we construct a comonad in pointed topological spaces endowed with the wedge product. We then prove an approxi
Externí odkaz:
http://arxiv.org/abs/2210.00839
We develop the basic theory of Maurer-Cartan simplicial sets associated to (shifted complete) $L_\infty$ algebras equipped with the action of a finite group. Our main result asserts that the inclusion of the fixed points of this equivariant simplicia
Externí odkaz:
http://arxiv.org/abs/2203.03200
We prove that the simplicial cocommutative coalgebra of singular chains on a connected topological space determines the homotopy type rationally and one prime at a time, without imposing any restriction on the fundamental group. In particular, the fu
Externí odkaz:
http://arxiv.org/abs/2006.05362
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We study the Eckmann-Hilton dual of the little disks algebra structure on iterated loop spaces: With the right definitions, every $n$-fold suspension is a coalgebra over the little $n$-disks operad. This structure induces non-trivial cooperations on
Externí odkaz:
http://arxiv.org/abs/1909.11043
Publikováno v:
Algebr. Geom. Topol. 21 (2021) 1535-1552
Bousfield and Kan's $\mathbb{Q}$-completion and fiberwise $\mathbb{Q}$-completion of spaces lead to two different approaches to the rational homotopy theory of non-simply connected spaces. In the first approach, a map is a weak equivalence if it indu
Externí odkaz:
http://arxiv.org/abs/1906.03655
Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg algebras. This answers a folklore problem in rational homotopy theory,
Externí odkaz:
http://arxiv.org/abs/1904.03585