[HTML][HTML] The diffeology of Milnor's classifying space
We define a diffeology on the Milnor classifying space of a diffeological group G, constructed
in a similar fashion to the topological version using an infinite join. Besides obtaining the …
in a similar fashion to the topological version using an infinite join. Besides obtaining the …
Kadomtsev-Petviashvili hierarchies with non-formal pseudo-differential operators, non-formal solutions, and a Yang-Mills--like formulation
JP Magnot, EG Reyes - arXiv preprint arXiv:2409.13771, 2024 - arxiv.org
We start from the classical Kadomtsev-Petviashvili hierarchy posed on formal pseudo-
differential operators, and we produce two hierarchies of non-linear equations posed on non …
differential operators, and we produce two hierarchies of non-linear equations posed on non …
The Cauchy problem of the Kadomtsev-Petviashvili hierarchy and infinite-dimensional groups
JP Magnot, EG Reyes - Nonlinear Systems and Their Remarkable …, 2019 - taylorfrancis.com
We introduce basic concepts of generalized Differential Geometry of Frölicher and
diffeological spaces; we consider formal and non-formal pseudodifferential operators in one …
diffeological spaces; we consider formal and non-formal pseudodifferential operators in one …
On the geometry of pseudodifferential operators based on renormalized traces
JP Magnot - arXiv preprint arXiv:2007.00387, 2020 - arxiv.org
In this article, we examine the geometry of a group of Fourier-integral operators, which is the
central extension of $ Diff (S^ 1) $ with a group of classical pseudo-differential operators of …
central extension of $ Diff (S^ 1) $ with a group of classical pseudo-differential operators of …
On the Kadomtsev-Petviashvili hierarchy in an extended class of formal pseudo-differential operators
JP Magnot, VN Roubtsov - Theoretical and Mathematical Physics, 2021 - Springer
We study the existence and uniqueness of the Kadomtsev–Petviashvili (KP) hierarchy
solutions in the algebra of formal classical pseudodifferential operators. The classical …
solutions in the algebra of formal classical pseudodifferential operators. The classical …
[PDF][PDF] Diff+(S1)− pseudo-differential operators and the Kadomtsev-Petviashvili hierarchy
JP Magnot, EG Reyes - arXiv preprint ArXiv:1808.03791 - hal.science
We establish a non-formal link between the structure of the group of Fourier integral
operators Cl0,* odd (S1, V) Diff+(S1) and the solutions of the Kadomtsev-Petviashvili …
operators Cl0,* odd (S1, V) Diff+(S1) and the solutions of the Kadomtsev-Petviashvili …
On the geometry of diffeological vector pseudo-bundles and infinite dimensional vector bundles: automorphisms, connections and covariant derivatives
JP Magnot - arXiv preprint arXiv:2207.06824, 2022 - arxiv.org
We consider here the category of diffeological vector pseudo-bundles, and study a possible
extension of classical differential geometric tools on finite dimensional vector bundles …
extension of classical differential geometric tools on finite dimensional vector bundles …
On diffeological principal bundles of non-formal pseudo-differential operators over formal ones
JP Magnot - arXiv preprint arXiv:2207.07015, 2022 - arxiv.org
We describe the structure of diffeological bundle of non formal classical pseudo-differential
operators over formal ones, and its structure group. For this, we give few results on …
operators over formal ones, and its structure group. For this, we give few results on …
On a class of closed cocycles for algebras of non-formal, possibly unbounded, pseudodifferential operators
JP Magnot - arXiv preprint arXiv:2012.06941, 2020 - arxiv.org
In this article, we consider algebras $\mathcal {A} $ of non-formal pseudodifferential
operators over $ S^ 1$ which contain $ C^\infty (S^ 1), $ understood as multiplication …
operators over $ S^ 1$ which contain $ C^\infty (S^ 1), $ understood as multiplication …
On the Cauchy problem for a Kadomtsev-Petviashvili hierarchy on non-formal operators and its relation with a group of diffeomorphisms
JP Magnot, EG Reyes - arXiv preprint arXiv:1808.03791, 2018 - arxiv.org
We establish a rigorous link between infinite-dimensional regular Fr\" olicher Lie groups built
out of non-formal pseudodifferential operators and the Kadomtsev-Petviashvili hierarchy. We …
out of non-formal pseudodifferential operators and the Kadomtsev-Petviashvili hierarchy. We …