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C∞-Algebraic Geometry with Corners
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.
Riemannian Holonomy Groups and Calibrated Geometry
This graduate level text covers an exciting and active area of research at the crossroads of several different fields in Mathematics and Physics. In Mathematics it involves Differential Geometry, Complex Algebraic Geometry, Symplectic Geometry, and in Physics String Theory and Mirror Symmetry. Drawing extensively on the author's previous work, the text explains the advanced mathematics involved simply and clearly to both mathematicians and physicists. Starting with the basic geometry of connections, curvature, complex and Kähler structures suitable for beginning graduate students, the text covers seminal results such as Yau's proof of the Calabi Conjecture, and takes the reader all the way to the frontiers of current research in calibrated geometry, giving many open problems.
Compact Manifolds with Special Holonomy
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.
Algebraic Geometry over C∞-Rings
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. Th...
Joyce's Politics
The object of this study, first published in 1980, is to dispel the view that James Joyce had no political views. Although not a political novelist like D. H. Lawrence or Joseph Conrad, political issues and discussions are central to Joyce’s major novels. This title links that political content with Joyce’s own views, and examines the evolution of those views and attitudes. A number of unusual and fascinating sources for Joyce’s thought are uncovered. Joyce’s Politics is thus a thorough review of a neglected aspect of Joyce and his writings, and will be of interest to students of literature.
Riemannian Holonomy Groups and Calibrated Geometry
Covering an exciting and active area of research at the crossroads of several different fields in mathematics and physics, and drawing on the author's previous work, this text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.
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 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 at...
Joyce, Bakhtin, and Popular Literature
The sheer mass of allusion to popular literature in the writings of James Joyce is daunting. Using theories developed by Russian critic Mikhail Bakhtin, R. B. Kershner analyzes how Joyce made use of popular literature in such early works as Stephen Hero, Dubliners, A Portrait of an Artist as a Young Man, and Exiles. Kershner also examines Joyce's use of rhetoric, the relationship between narrator and protagonist, and the interplay of voices, whether personal, literary, or subliterary, in Joyce's writing. In pointing out the prolific allusions in Joyce to newspapers, children's books, popular novels, and even pornography, Kershner shows how each of these contributes to the structures of consc...
Routledge Library Editions: James Joyce
This set reissues 8 books on James Joyce originally published between 1966 and 1991. The volumes examine many of Joyce’s most respected works, including Finnegans Wake, Dubliners and Ulysses. As well as providing an in-depth analyses of Joyce’s work, this collection also looks at James Joyce in the context of the Modernist movement as a whole. This set will be of particular interest to students of literature.
Calabi-Yau Manifolds and Related Geometries
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
