Spin Manifoldsmath.DG
New -manifolds studied for their properties.
problem Understanding new manifold classifications.
method Exploring -manifolds as a new category.
result Highlights of -manifolds discussed.
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48 results for “Spin Manifolds”
The paper explores spin^h structures and their obstructions.
problem Understanding which manifolds are spin^h.
method Analyzing the fifth Stiefel-Whitney class and constructing generalised spin structures.
result Every compact orientable manifold of dimension 7 or lower is spin^h, and there are higher-dimensional manifolds that are not.
New -instantons constructed on Joyce's manifold.
problem Constructing -instantons on Joyce's compact manifold.
method Gluing non-flat connections on local model spaces to a flat connection on the -orbifold.
result More than 20,000 new four-parameter families of -instantons.
Proves almost flat spin^c manifolds bound compact manifolds.
problem Proving almost flat spin^c manifolds bound compact manifolds.
method Long-standing conjecture of Farrell--Zdravkovska and S. T. Yau settled.
result Every almost flat spin^c manifold bounds a compact orientable manifold.
Study of higher spin Killing spinors on 3D manifolds, proving rigidity and providing explicit expressions.
problem Understanding higher spin Killing spinors on 3D manifolds.
method Definition and detailed study of higher spin Killing spinors in arbitrary dimension, focusing on 3D manifolds. Rigidity result and explicit expressions for 3-sphere and 3-hyperbolic space.
result Proved a rigidity result for 3D manifolds admitting higher spin Killing spinors and provided explicit expressions for these spinors.
Study on harmonic flow of Spin(7)-structures in 8D manifolds.
problem Comparing isometric Spin(7)-structures.
method Developed a notion of harmonicity for Spin(7)-structures and studied the harmonic flow.
result Analytical properties of the harmonic flow of Spin(7)-structures presented.
Study shows certain spin manifolds can't meet DEC condition.
problem Non-existence of spin fill-ins meeting DEC condition.
method Analyzes spin Riemannian manifolds and generalized mean curvature functions.
result Closed spin manifolds cannot satisfy DEC if curvature is large.
Real vector bundles are determined by their Dirac indices on specific spin manifolds.
problem Determining real vector bundles using Dirac indices.
method Mapping spin or spin manifolds into a compact smooth manifold and using Dirac indices.
result Real vector bundles are uniquely determined by their Dirac indices on prescribed manifolds.
Rigidity of elliptic genera proven for non-spin manifolds with -action.
problem Rigidity of elliptic genera for non-spin manifolds with -action.
method Analysis of universal covering spin condition and for rigidity.
result Rigidity of elliptic genera is proven for spin universal coverings but not for non-spin universal coverings.
Study -dDT connections on manifolds with -structures.
problem Understanding moduli spaces of -dDT connections.
method Introduced and studied -dDT connections using fully nonlinear PDEs.
result Moduli space has finite expected dimension and smoothness under certain conditions.
No spin structures found in a hyperbolic 4D space.
problem Finding hyperbolic 4-manifolds without spin structures.
method Constructed a non-compact, orientable, hyperbolic 4-manifold.
result Demonstrated existence of a hyperbolic 4D space without spin structures.
No Hantzsche-Wendt manifolds over 3D admit spin^c structures.
problem Existence of spin^c structures on Hantzsche-Wendt manifolds.
method Combinatorial description of Stiefel-Whitney classes for closed flat manifolds.
result No Hantzsche-Wendt manifold of dimension greater than three admits a spin^c structure.
New rigidity theorems for spin^c manifolds using modular invariance.
problem Establishing rigidity theorems for twisted Dirac and Toeplitz operators.
method Liu's modular invariance method and its odd-dimensional extension.
result New Witten rigidity theorems for even and odd-dimensional spin^c manifolds.
Study proves a conjecture for certain spin manifolds.
problem Proving a conjecture about positive scalar curvature metrics.
method Connected sum construction and Gromov-Lawson area enlargement.
result Connected sum of spin manifolds admits no complete metric of positive scalar curvature.
New invariant for spin 3-manifolds using super 3-cocycles.
problem Constructing an invariant for spin 3-manifolds.
method State sum construction based on super 3-cocycles and combinatorial representation.
result The invariant is sensitive to the spin structure.
The paper studies curvature identities and solitons on Spin(7)-manifolds.
problem Curvature identities and solitons on Spin(7)-manifolds.
method Analyzes the curvature and torsion of Spin(7)-manifolds, proving identities and conditions.
result Conditions for closed torsion and implications for Ricci flatness and solitons.
We study spin structures on compact simply-connected homogeneous pseudo-Riemannian manifolds (M = G/H, g) of a compact semisimple Lie group G. We classify flag manifolds F = G/H of a compact simple Lie group which are spin. This yields also the classification of all flag manifolds carrying an invariant metaplectic stru…
This paper gives a combinatorial description of spin and spin^c-structures on triangulated PL-manifolds of arbitrary dimension. These formulations of spin and spin^c-structures are established primarily for the purpose of aiding in computations. The novelty of the approach is we rely heavily on the naturality of binary…
In this paper, we extend the study of generalized Killing spinors on Riemannian Spin manifolds started by Moroianu and Herzlich to complex Killing functions. We prove that such spinor fields are always real Spin Killing spinors or imaginary generalized Spin Killing spinors, providing that the dimension of t…
A homotopy classification of -structures with applications to exceptional Riemannian holonomymath.DG
Classifies Spin(7) structures on compact 8-manifolds with abelian fundamental group.
problem Classifying Spin(7) structures on compact 8-manifolds.
method Obstruction theory applied to Spin(7) structures on compact 8-manifolds with abelian fundamental group.
result Compact Riemannian 8-manifolds with holonomy Spin(7) have exactly two Spin(7) structures extending the induced G2 structure on the boundary.
Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi-Yau four-orbifold divided by an anti-holomorphi…
Paper computes G-index for specific hyperbolic manifolds.
problem Computing G-index for closed, spin, hyperbolic manifolds.
method Developed techniques to compute G-index for 2- or 4-manifolds.
result Computed G-index for Davis hyperbolic 4-manifold.
We derive various pinching results for small Dirac eigenvalues using the classification of and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for manifolds which involves a general study on convergence of Riemannian manifolds with a pr…
Study on instantons in and manifolds.
problem Investigate instanton properties in and manifolds.
method Analyze the characteristic and torsion connections on and manifolds, focusing on parallel torsion and Lee forms.
result Conditions for the curvature of the characteristic connection to be a instanton and for the torsion connection to be a instanton are established.
The study explores psc-metrics on non-spin manifolds with pin^\pm or spin^c structures.
problem Existence of psc-metrics on non-spin manifolds with specific structures.
method Analysis of Dirac operators and index theory on pin^\pm or spin^c manifolds.
result The index of a Dirac operator controls the existence of psc-metrics on certain manifolds.
Study on nonspin manifolds with spin boundary, showing nonconnectedness and nontrivial fundamental group.
problem Understanding spaces of positive scalar curvature metrics on totally nonspin manifolds.
method Analysis of positive scalar curvature metrics on manifolds with spin boundary, using propagation techniques.
result Spaces of positive scalar curvature metrics are not connected and have nontrivial fundamental groups for certain dimensions.
Study calculates deformations of instantons on a specific -manifold.
problem Analyzing instantons on a specific -manifold.
method Deformation theory developed by the author.
result Virtual dimensions of moduli spaces of instantons calculated.
We study the Rarita-Schwinger operator on compact Riemannian spin manifolds. In particular, we find examples of compact Einstein manifolds with positive scalar curvature where the Rarita-Schwinger operator has a non-trivial kernel. For positive quaternion Kähler manifolds and symmetric spaces with spin structure we giv…
A Short Proof of the Localization Formula for the Loop Space Chern Character of Spin Manifoldsmath.DG
Short proof given for a complex formula in spin manifold geometry.
problem Localization formula for loop space Chern character in spin manifolds.
method Using rescaled spinor bundle on tangent groupoid.
result A concise proof of the localization formula.
We show that many spin 6-manifolds have the homotopy type but not the homeomorphism type of a Kaehler manifold. Moreover, for given Betti numbers, there are only finitely many deformation types and hence topological types of smooth complex projectve spin threefolds of general type. Finally, on a fixed spin 6-manifold, …
Study shows infinitely many path components for positive Ricci curvature metrics on certain spin manifolds.
problem Understanding the space of metrics with positive Ricci curvature on spin manifolds.
method Analyzing spin manifolds of dimension 4k-1 for k ≥ 2, focusing on metrics with a specific property.
result The space of metrics has infinitely many path components.
Cobordism and signatures of manifolds with similar fundamental groups.
problem Understanding cobordism and signatures of manifolds with specific fundamental groups.
method Analyzing smooth closed connected aspherical manifolds with good fundamental groups.
result Cobordism and signatures of manifolds are preserved under certain conditions on their fundamental groups.
Spin-structures on real Bott manifolds with Kähler structure are characterized.
problem Existence of spin-structures on real Bott manifolds with Kähler structure.
method Ishida characterization and techniques from \cite{PS16} using characteristic classes.
result Necessary and sufficient condition for the existence of spin-structures on .
Constructs modular forms and proves divisibility results for odd-dimensional manifolds.
problem Constructing modular forms over specific groups and proving divisibility results.
method SL(2, Z) modular forms and Witten genus in odd dimensions.
result Obtained divisibility results of index of Toeplitz operators on spin and spin^c manifolds.
In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are in one to one correspondence with lifts to Spin_n of the Riemannian …
Proves positive mass theorem for non-spin weighted manifolds.
problem Proving the positive mass theorem for non-spin weighted manifolds.
method Establishing density theorem and generalizing Geroch conjecture.
result Proves positive weighted mass theorem for non-spin weighted manifolds.
We show how the space of complex spin structures of a closed oriented three-manifold embeds naturally into a space of quadratic functions associated to its linking pairing. Besides, we extend the Goussarov-Habiro theory of finite type invariants to the realm of compact oriented three-manifolds equipped with a complex s…
Simplified proof of spin^c structures using twistor spaces.
problem Proving every compact oriented 4-manifold admits spin^c structures.
method Using twistor spaces to provide a simpler, more geometric proof.
result Simplified and clarified understanding of spin^c structures in 4-manifolds.
Paper solves long neck problem on odd-dimensional spin manifolds.
problem Long neck problem on odd-dimensional spin manifolds.
method Spectral flow of Callias operators.
result Complete answer to Gromov's long neck problem.
We define spin frames, with the aim of extending spin structures from the category of (pseudo-)Riemannian manifolds to the category of spin manifolds with a fixed signature on them, though with no selected metric structure. Because of this softer requirements, transformations allowed by spin frames are more general tha…
Study instantons on asymptotically conical Spin(7)-manifolds, identifying deformation spaces.
problem Deformation theory of instantons on specific Spin(7)-manifolds.
method Relating deformation complex to spinors, identifying kernel of twisted negative Dirac operator.
result Virtual dimension of moduli space calculated using index theorem and Dirac operator spectrum.
New formulas derived from modular forms for manifold indices.
problem Calculating indices of twisted Dirac operators on manifolds.
method SL(2, Z) modular forms and Γ^0(2), Γ_0(2) forms.
result New anomaly cancellation formulas for spin and spin^c manifolds.
This paper explores 4-planes in Spin(7) manifolds with symplectic structures.
problem Characterizing 4-planes in Spin(7) manifolds with symplectic structures.
method Detailed analysis of differential forms, including the Cayley 4-form, and exploration of mirror duality.
result Enhanced understanding of the interplay between Spin(7)-structures and symplectic geometry.
Study invariant spin^r structures on homogeneous spaces.
problem Classify invariant spin^r structures on homogeneous spaces.
method Introduce and study -invariance of spin^r structures on homogeneous spaces.
result Classification of invariant spin^r structures in terms of isotropy representation.
We show the existence of nonsymmetric homogeneous spin Riemannian manifolds whose Dirac operator is like that on a Riemannian symmetric spin space. Such manifolds are exactly the homogeneous spin Riemannian manifolds which are traceless cyclic with respect to some quotient expression and reductive decom…
New Spin(7) manifolds created from Calabi-Yau bundles.
problem Creating complete non-compact Spin(7) manifolds.
method Building on -bundles over AC Calabi-Yau manifolds.
result First known examples of complete toric Spin(7) manifolds.
We give a necessary and suffcient condition for almost-flat manifolds with cyclic holonomy to admit a Spin structure. Using this condition we find all 4-dimensional orientable almost- flat manifolds with cyclic holonomy that do not admit a Spin structure.
Classifies manifolds with specific spinors and constructs parallel spinors.
problem Classifying manifolds with generalized Killing spinors.
method Explicitly constructs parallel spinors and considers modified Dirac currents.
result Classifies Riemannian spin^c manifolds with type I and II imaginary generalized Killing spinors.