In this work, in two parts, we continue to develop the geometric theory of quantum PDE's, introduced by us starting from 1996. This theory has the purpose to build a rigorous mathematical theory of PDE's in the category $\mathfrak{D}_S$ of noncommutative manifolds ({\em quantum (super)manifolds}), necessary to encode physical phenomena at microscopic level (i.e., {\em quantum level}). Aim of the present paper is to report on some new issues in this direction, emphasizing an interplaying between surgery, integral bordism groups and conservations laws. In particular, a proof of the Poincar\'e conjecture, generalized to the category $\mathfrak{D}_S$, is given by using our geometric theory of PDE's just in such a category.

Surgery and bordism groups in quantum partial differential equations.I: The quantum Poincaré conjecture / Prastaro, Agostino. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 12:71(2009), pp. 502-525. [10.1016/j.na.2008.11.077]

Surgery and bordism groups in quantum partial differential equations.I: The quantum Poincaré conjecture

PRASTARO, Agostino
2009

Abstract

In this work, in two parts, we continue to develop the geometric theory of quantum PDE's, introduced by us starting from 1996. This theory has the purpose to build a rigorous mathematical theory of PDE's in the category $\mathfrak{D}_S$ of noncommutative manifolds ({\em quantum (super)manifolds}), necessary to encode physical phenomena at microscopic level (i.e., {\em quantum level}). Aim of the present paper is to report on some new issues in this direction, emphasizing an interplaying between surgery, integral bordism groups and conservations laws. In particular, a proof of the Poincar\'e conjecture, generalized to the category $\mathfrak{D}_S$, is given by using our geometric theory of PDE's just in such a category.
2009
Mathematical surgery; Integral bordism groups; Quantum PDE's; Quantum super PDE's; Quantum generalized Poincare' conjecture.
01 Pubblicazione su rivista::01a Articolo in rivista
Surgery and bordism groups in quantum partial differential equations.I: The quantum Poincaré conjecture / Prastaro, Agostino. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 12:71(2009), pp. 502-525. [10.1016/j.na.2008.11.077]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/36310
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