REVIEW 12 cited by
Generalized complex geometry
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field. We provide new examples, including some on manifolds admitting no known complex or symplectic structure. We prove a generalized Darboux theorem which yields a local normal form for the geometry. We show that there is an elliptic deformation theory and establish the existence of a Kuranishi moduli space. We then define the concept of a generalized Kahler manifold. We prove that generalized Kahler geometry is equivalent to a bi-Hermitian geometry with torsion first discovered by physicists. We then use this result to solve an outstanding problem in 4-dimensional bi-Hermitian geometry: we prove that there exists a Riemannian metric on the complex projective plane which admits exactly two distinct Hermitian complex structures with equal orientation. Finally, we introduce the concept of generalized complex submanifold, and show that such sub-objects correspond to D-branes in the topological A- and B-models of string theory.
Forward citations
Cited by 12 Pith papers
-
Poisson K-stability and the semiclassical Yau--Tian--Donaldson correspondence
Polystable Poisson structures on Kähler–Einstein Fano manifolds admit constant-scalar-curvature symplectic generalized Kähler metrics for small enough Poisson tensors, settling the semiclassical YTD conjecture on P².
-
On the Dirac complement problem
A new cohomology class obstructs the existence of Dirac complements, and for Lie algebras carrying a definite invariant pairing, the diagonal in g⊕ḡ admits a Dirac complement exactly when g is abelian — covering all r...
-
Coisotropic branes in symplectic manifolds
The authors develop a deformation theory for coisotropic branes, explicitly describing nearby branes in a codimension-one model and showing that the forgetful map from branes to coisotropic submanifolds is not locally...
-
$\alpha'$-Bootstrap
An infinite-dimensional algebraic structure on a megaspace yields recursive, T-duality-covariant NS-NS α' and α'^{2} corrections matching known bosonic and heterotic results up to field redefinitions.
-
On Quantum Aspects of 1-Form Symmetries I: BV-BRST Cohomology and Anomaly Polynomials
Develops Čech-de Rham bicomplex from gerbe data for BV-BRST cohomology of U(1) 2-form gauge theories and anomaly polynomials of 1-form symmetries.
-
Continuous Hochschild Cohomology and Formality
A continuous contraderived-category framework and formality theorems are proposed, but the foundational product/tensor-product lemma is false and the de Rham formality claim has a counterexample.
-
Gauged Extended Field Theory and Generalised Cartan Geometry
A systematic Cartan-geometric construction of linearised torsion and curvature hierarchies for generalised geometries with global duality group G and local gauge group H, realised via brane current algebras.
-
Off-shell double copy theories in BV
A BV-formalism construction gives off-shell double-copy actions for Chern-Simons, BF, and 2D Yang-Mills theories, with Kodaira-Spencer and Kähler gravity as natural examples.
-
New geometric structures on 3-manifolds: surgery and generalized geometry
Every closed orientable 3-manifold admits a stable B3-generalized complex structure.
-
On the triviality of the generalized tangent bundle
The generalized tangent bundle of a parallelizable manifold is trivial, but the converse does not hold, as shown by the Möbius strip, spheres, and projective spaces; it is also related to generalized geometric structures.
-
Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations
Tensionless p-branes and branes in degenerate-metric spacetimes admit symmetry transformations built from Killing tensors of arbitrary rank, extending string W-symmetries to all brane dimensions.
-
Compact Temporal Geometry and the $T^2$ Framework for Quantum Gravity
Time is modeled as a compact two-torus with a coherence direction whose string-scale compactification allegedly yields quantized temporal modes, UV regularization, and emergent classicality.
Discussion (0). Sign in to comment.