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Compact Manifolds with Special Holonomy
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existenceExpand
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A theory of generalized Donaldson–Thomas invariants
This book studies generalized Donaldson-Thomas invariants $\bar{DT}{}^\alpha(\tau)$. They are rational numbers which 'count' both $\tau$-stable and $\tau$-semistable coherent sheaves with ChernExpand
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COMPACT RIEMANNIAN 7-MANIFOLDS WITH HOLONOMY G2. I DOMINIC D. JOYCE
The list of possible holonomy groups of Riemannian manifolds given by Berger [3] includes three intriguing special cases, the holonomy groups G2, Spin(7) and Spin(9) in dimensions 7, 8 and 16Expand
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Compact Riemannian 7-manifolds with holonomy $G\sb 2$. II
This is the second of two papers about metrics of holonomy G2 on compact 7manifolds. In our first paper [15] we established the existence of a family of metrics of holonomy G2 on a single, compact,Expand
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COMPACT RIEMANNIAN 7-MANIFOLDS WITH HOLONOMY G2. II
This is the second of two papers about metrics of holonomy G2 on compact 7manifolds. In our first paper [15] we established the existence of a family of metrics of holonomy G2 on a single, compact,Expand
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Riemannian Holonomy Groups And Calibrated Geometry
The holonomy group Hol(g) of a Riemannian n-manifold (M, g) is a global invariant which measures the constant tensors on the manifold. It is a Lie subgroup of SO(n), and for generic metrics Hol(g) =Expand
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MOTIVIC INVARIANTS OF ARTIN STACKS AND ‘STACK FUNCTIONS’
An invariant I of quasiprojective K-varieties X with values in a commutative ring R is "motivic" if I(X)= I(Y)+I(X\Y) for Y closed in X, and I(X x Y)=I(X)I(Y). Examples include Euler characteristicsExpand
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Compact 8-manifolds with holonomy Spin(7)
In Berger’s classification [4] of the possible holonomy groups of a nonsymmetric, irreducible riemannian manifold, there are two special cases, the exceptional holonomy groups G2 in 7 dimensions andExpand
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Immersed Lagrangian Floer Theory
Let (M,w) be a compact symplectic manifold, and L a compact, embedded Lagrangian submanifold in M. Fukaya, Oh, Ohta and Ono construct Lagrangian Floer cohomology for such M,L, yielding groupsExpand
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On manifolds with corners
Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have receivedExpand
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