H2020Индивидуална стипендия2018–2021

GENERALIZED · Generalized geometry: 3-manifolds and applications

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2018-09-01 → 2021-10-31
Финансиране от ЕС: 170 122 €
Участници: 1
Схема: MSCA-IF-EF-ST

Линиите свързват координатора с партньорите.

Накратко на български

Обобщената геометрия изследва математически структури в пространства с различна размерност, като например триизмерните многообразия. Тя помага за обединяване на различни геометрични теории и създаване на нови рамки за описанието на пространството.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Generalized geometry: 3-manifolds and applications

Generalized geometry is a revolutionary approach to geometric structures with the power of providing suitable mathematical frameworks, unifying theories, and defining interesting new structures. Thus, generalized Kähler geometry is the most convenient language for bihermitian geometry, whereas generalized complex geometry unifies symplectic and complex geometry but there are manifolds that are neither complex nor symplectic and admit a generalized complex structure. This generalized complex structure has type change, the phenomenon that makes generalized geometry unique. Both generalized Kähler and complex geometry are only possible for even-dimensional manifolds. What can generalized geometry offer for odd-dimensional manifolds? What about the case of three-manifolds? What can we do with generalized geometry?

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

Generalized geometry is a revolutionary approach to geometric structures pioneered by Hitchin in 2003, soon becoming an active topic catching the interest and bringing together the expertise of geometers and theoretical physicists. Generalized complex structures, defined for even-dimensional manifolds, are both a genuinely interesting mathematical structure, providing insight of complex and symplectic geometry, and the suitable notion for some physical theories like mirror symmetry. Odd-dimensional manifolds within generalized geometry have not been satisfactorily studied until the recent introduction of generalized geometry of type Bn and its study in my PhD thesis. There, the case of 3-manifolds drew special attention thanks to the recent Thurston's geometrization theorem and the fact that the type-change locus of a 3-manifold is a link, bringing in knot and link theory. This action combines the generalized geometry expertise of the experienced researcher with the host’s expertise on 3-manifold and knot and link theory in order to set a novel geometrical framework for structures on odd-dimensional manifolds, understand the case of 3-manifolds in depth, and create a two-way bridge between these previously unrelated areas, with innovative applications in both.

Оригинален текст от CORDIS (на английски).

Участници

UNIVERSITAT AUTONOMA DE BARCELONA · Cerdanyola Del VallesКоординаторИспания