58Bxx Infinite-dimensional manifolds
This subtopic introduces the core ideas in infinite-dimensional manifolds, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Specific topics
58B05 Homotopy and topological questions for infinite-dimensional manifolds
Overview
Homotopy and topological questions for infinite-dimensional manifolds. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks
58B10 Differentiability questions for infinite-dimensional manifolds
Overview
Differentiability questions for infinite-dimensional manifolds. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks
58B12 Questions of holomorphy for bodies of infinite-dimensional manifolds
Overview
Questions of holomorphy for bodies of infinite-dimensional manifolds. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks
58B15 Fredholm structures on infinite-dimensional manifolds
Overview
Fredholm structures on infinite-dimensional manifolds. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
Overview
Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks
58B25 Group structures and generalizations on infinite-dimensional manifolds
Overview
Group structures and generalizations on infinite-dimensional manifolds. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks
58B32 Geometry of quantum groups
Overview
Geometry of quantum groups. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks
58B34 Noncommutative geometry in global analysis
Overview
Noncommutative geometry in global analysis. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks
58B40 Diffeology
Overview
Diffeology. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks
58B99 None of the above
Overview
None of the above. This topic studies infinite-dimensional manifolds modeled on Banach, Hilbert, and related spaces, including smooth and geometric structures.
Related Wikipedia Page
Wikipedia: Banach manifold
Useful Links
Key Ideas
- infinite-dimensional charts and smoothness
- functional-analytic manifold models
- geometry beyond finite dimensions
Typical Uses
Used in variational analysis, PDE, and geometric frameworks where configuration spaces are infinite-dimensional.
Applications
- Global analysis
- Field theory configuration spaces
- Nonlinear functional geometry
References
Recommended Textbooks