Results 31 to 40 of about 59,724 (184)

Smooth approximations and their applications to homotopy types

Pracì Mìžnarodnogo Geometričnogo Centru, 2020
Let $M, N$ the be smooth manifolds, $\mathcal{C}^{r}(M,N)$ the space of ${C}^{r}$ maps endowed with the corresponding weak Whitney topology, and $\mathcal{B} \subset \mathcal{C}^{r}(M,N)$ an open subset.
Олександра Олександрівна Хохлюк, Sergiy Ivanovych Maksymenko   +1 more
doaj   +1 more source

The homotopy fixed point set of Lie group actions on elliptic spaces

, 2014
Let $G$ be a compact connected Lie group, or more generally a path connected topological group of the homotopy type of a finite CW-complex, and let $X$ be a rational nilpotent $G$-space.
Buijs, Urtzi, Félix, Yves, Huerta, Sergio, Murillo, Aniceto   +3 more
core   +1 more source

Automorphism groups of polycyclic-by-finite groups and arithmetic groups [PDF]

, 2005
We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic
A. Borel, A. Borel, A. Borel, B.A.F. Wehrfritz, B.A.F. Wehrfritz, D. Segal, D. Sullivan, D. Sullivan, F. Grunewald, F. Grunewald, F. Grunewald, F. Grunewald, F. Grunewald, F. Grunewald, F. Grunewald, Fritz Grunewald, G. Baumslag, G. Baumslag, G.D. Mostow, G.D. Mostow, I. Ju. Merzljakov, J. Roitberg, J.-L. Koszul, J.-P. Serre, K. Nomizu, K.S. Brown, L. Auslander, L. Auslander, L. Auslander, L. Auslander, L.A. Lambe, M. du Sautoy, O. Baues, O. Baues, Oliver Baues, P. Deligne, P.A. Griffiths, P.F. Pickel, R.M. Bryant, S. Maclane, V.A. Romankov   +40 more
core   +3 more sources

Stable homotopy groups of spheres [PDF]

Proceedings of the National Academy of Sciences, 2020
SignificanceThe geometric objects of interest in algebraic topology can be constructed by fitting together spheres of varying dimensions. The homotopy groups of spheres describe the ways in which spheres can be attached to each other. From the viewpoint of algebraic topology, detailed knowledge of these groups would lead to a classification of ...
Daniel C. Isaksen, Guozhen Wang, Zhouli Xu   +2 more
openaire   +3 more sources

Omega vs. pi, and 6d anomaly cancellation

Journal of High Energy Physics, 2021
In this note we review the role of homotopy groups in determining non-perturbative (henceforth ‘global’) gauge anomalies, in light of recent progress understanding global anomalies using bordism.
Joe Davighi, Nakarin Lohitsiri
doaj   +1 more source

Higher homotopy of groups definable in o-minimal structures

, 2009
It is known that a definably compact group G is an extension of a compact Lie group L by a divisible torsion-free normal subgroup. We show that the o-minimal higher homotopy groups of G are isomorphic to the corresponding higher homotopy groups of L.
Berarducci, Alessandro, Mamino, Marcello, Otero, Margarita   +2 more
core   +2 more sources

A Perspective on Interactive Theorem Provers in Physics

Advanced Science, EarlyView.
Into an interactive theorem provers (ITPs), one can write mathematical definitions, theorems and proofs, and the correctness of those results is automatically checked. This perspective goes over the best usage of ITPs within physics and motivates the open‐source community run project PhysLean, the aim of which is to be a library for digitalized physics
Joseph Tooby‐Smith
wiley   +1 more source

Secondary homotopy groups [PDF]

Forum Mathematicum, 2008
Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic models of homotopy types with homotopy groups concentrated in two consecutive dimensions.
Baues, Hans Joachim, Muro Jiménez, Fernando   +1 more
openaire   +4 more sources

Metasurfaces and Metadevices for Topological Electromagnetic Waves

Advanced Physics Research, EarlyView.
Optical topologies refer to diverse topological localized structures made by diverse parameters of light fields, such as vortices, skyrmions, and hopfions. This article navigates a direction of metasurface‐based integrated devices for generation, manipulation and detection of novel topologies of light, which would be a rapidly growing interdisciplinary
Rensheng Xie, Nilo Mata‐Cervera, Xi Xie, Yijie Shen   +3 more
wiley   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source