Dominic D. Joyce's Books

Compact Manifolds with Special Holonomy

By: Dominic D. Joyce

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Compact Manifolds with Special Holonomy

By: Dominic D. Joyce

This is a combination of a graduate textbook on Reimannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It contains much new research and many new examples.

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Page Count

460

Publisher

OUP Oxford

Published Date

ISBN 10

0198506015

ISBN 13

9780198506010

A Theory of Generalized Donaldson-Thomas Invariants

By: Dominic D. Joyce,Yinan Song

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A Theory of Generalized Donaldson-Thomas Invariants

By: Dominic D. Joyce,Yinan Song

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 Chern character $\alpha$ on $X$; strictly $\tau$-semistable sheaves must be counted with complicated rational weights. The $\bar{DT}{}^\alpha(\tau)$ are defined for all classes $\alpha$, and are equal to $DT^\alpha(\tau)$ when it is defined. They are unchanged under deformations of $X$, and transform by a wall-crossing formula under change of stability condition $\tau$. To prove all this, the authors study the local structure of the moduli stack $\mathfrak M$ of coherent sheaves on $X$. They show that an atlas for $\mathfrak M$ may be written locally as $\mathrm{Crit}(f)$ for $f:U\to{\mathbb C}$ holomorphic and $U$ smooth, and use this to deduce identities on the Behrend function $\nu_\mathfrak M$. They compute the invariants $\bar{DT}{}^\alpha(\tau)$ in examples, and make a conjecture about their integrality properties. They also extend the theory to abelian categories $\mathrm{mod}$-$\mathbb{C}Q\backslash I$ of representations of a quiver $Q$ with relations $I$ coming from a superpotential $W$ on $Q$.

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Page Count

212

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821852795

ISBN 13

9780821852798

Riemannian Holonomy Groups and Calibrated Geometry

By: Dominic D. Joyce

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Riemannian Holonomy Groups and Calibrated Geometry

By: Dominic D. Joyce

Riemannian Holonomy Groups and Calibrated Geometry covers an exciting and active area of research at the crossroads of several different fields in mathematics and physics. Drawing on the author's previous work the text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.

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Page Count

314

Publisher

Oxford University Press

Published Date

ISBN 10

019921560X

ISBN 13

9780199215607

Algebraic Geometry over C∞-Rings

By: Dominic Joyce

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Algebraic Geometry over C∞-Rings

By: Dominic Joyce

If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.

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Page Count

152

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470436450

ISBN 13

9781470436452

C∞-Algebraic Geometry with Corners

By: Kelli Francis-Staite,Dominic Joyce

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C∞-Algebraic Geometry with Corners

By: Kelli Francis-Staite,Dominic Joyce

Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.

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Page Count

224

Publisher

Cambridge University Press

Published Date

ISBN 10

1009400207

ISBN 13

9781009400206

Virtual Fundamental Cycles in Symplectic Topology

By: John W. Morgan,Dusa McDuff,Mohammad Tehrani,Kenji Fukaya,Dominic Joyce

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Virtual Fundamental Cycles in Symplectic Topology

By: John W. Morgan,Dusa McDuff,Mohammad Tehrani,Kenji Fukaya,Dominic Joyce

The method of using the moduli space of pseudo-holomorphic curves on a symplectic manifold was introduced by Mikhail Gromov in 1985. From the appearance of Gromov's original paper until today this approach has been the most important tool in global symplectic geometry. To produce numerical invariants of these manifolds using this method requires constructing a fundamental cycle associated with moduli spaces. This volume brings together three approaches to constructing the “virtual” fundamental cycle for the moduli space of pseudo-holomorphic curves. All approaches are based on the idea of local Kuranishi charts for the moduli space. Workers in the field will get a comprehensive understanding of the details of these constructions and the assumptions under which they can be made. These techniques and results will be essential in further applications of this approach to producing invariants of symplectic manifolds.

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Page Count

317

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470450143

ISBN 13

9781470450144

Globalizing Cricket

Englishness, Empire and Identity

By: Dominic Malcolm

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Globalizing Cricket

Englishness, Empire and Identity

By: Dominic Malcolm

This book is available as open access through the Bloomsbury Open Access programme and is available on www.bloomsburycollections.com. Globalizing Cricket examines the global role of the sport - how it developed and spread around the world. The book explores the origins of cricket in the eighteenth century, its establishment as England's national game in the nineteenth, the successful (Caribbean) and unsuccessful (American) diffusion of cricket as part of the development of the British Empire and its role in structuring contemporary identities amongst and between the English, the British and postcolonial communities. Whilst empirically focused on the sport itself, the book addresses broader issues such as social development, imperialism, race, diaspora and national identities. Tracing the beginnings of cricket as a 'folk game' through to the present, it draws together these different strands to examine the meaning and social significance of the modern game. This book is a must-read for anyone interested in the role of sport in both colonial and post-colonial periods; the history and peculiarities of English national identity; or simply intrigued by the game and its history.

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Page Count

192

Publisher

A&C Black

Published Date

ISBN 10

1849665613

ISBN 13

9781849665612

Calabi-Yau Manifolds and Related Geometries

Lectures at a Summer School in Nordfjordeid, Norway, June 2001

By: Mark Gross,Daniel Huybrechts,Dominic Joyce

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Calabi-Yau Manifolds and Related Geometries

Lectures at a Summer School in Nordfjordeid, Norway, June 2001

By: Mark Gross,Daniel Huybrechts,Dominic Joyce

This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results. From the reviews: "An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book." --MATHEMATICAL REVIEWS

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Page Count

245

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642190049

ISBN 13

9783642190049

Book's by Dominic D. Joyce

Compact Manifolds with Special Holonomy

Compact Manifolds with Special Holonomy

A Theory of Generalized Donaldson-Thomas Invariants

A Theory of Generalized Donaldson-Thomas Invariants

Riemannian Holonomy Groups and Calibrated Geometry

Riemannian Holonomy Groups and Calibrated Geometry

Algebraic Geometry over C∞-Rings

Algebraic Geometry over C∞-Rings

C∞-Algebraic Geometry with Corners

C∞-Algebraic Geometry with Corners

Virtual Fundamental Cycles in Symplectic Topology

Virtual Fundamental Cycles in Symplectic Topology

Globalizing Cricket

Globalizing Cricket

Calabi-Yau Manifolds and Related Geometries

Calabi-Yau Manifolds and Related Geometries

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