By various, Huai-Dong Cao (Lehigh University), Shing-Tung Yau (Harvard University)

ISBN-10: 1571461388

ISBN-13: 9781571461384

Contents exact Lagrangian fibrations, wall-crossing, and replicate symmetry (Denis Auroux) Sphere theorems in geometry (Simon Brendle and Richard Schoen) Geometric Langlands and non-Abelian Hodge conception (Ron Donagi and Tony Pantev) advancements round confident sectional curvature (Karsten Grove) Einstein metrics, four-manifolds, and conformally Kähler geometry (Claude LeBrun) lifestyles of Faddeev knots (Fengbo hold, Fanghua Lin, and Yisong Yang) Milnor K2 and box homomorphisms (Fedor Bogomolov and Yuri Tschinkel) Arakelov inequalities (Eckart Viehweg) A survey of Calabi-Yau manifolds (Shing-Tung Yau)

Show description

Read Online or Download Surveys in Differential Geometry (Volume 13): Geometry, Analysis and Algebraic Geometry PDF

Similar differential geometry books

New PDF release: The topology of fibre bundles

Fibre bundles, now an essential component of differential geometry, also are of significant value in sleek physics - akin to in gauge conception. This publication, a succinct advent to the topic by way of renown mathematician Norman Steenrod, used to be the 1st to offer the topic systematically. It starts off with a basic creation to bundles, together with such subject matters as differentiable manifolds and masking areas.

Get Differential geometry and complex analysis: a volume PDF

Chavel I. , Farkas H. M. (eds. ) Differential geometry and complicated research (Springer, 1985)(ISBN 354013543X)(236s)

Download PDF by Leon Simon: Theorems on regularity and singularity of energy minimizing

The purpose of those lecture notes is to offer an primarily self-contained advent to the elemental regularity concept for strength minimizing maps, together with contemporary advancements about the constitution of the singular set and asymptotics on method of the singular set. really good wisdom in partial differential equations or the geometric calculus of diversifications is no longer required.

Additional resources for Surveys in Differential Geometry (Volume 13): Geometry, Analysis and Algebraic Geometry

Sample text

The formulation which is the most relevant to us is the one discussed by Abouzaid in [1]: in this version, one considers Lagrangian sub manifolds of XV with boundary contained in the given reference fiber D V = W-1(e t ), and which near the reference fiber are mapped by W to an embedded curve C. 3. +. Floer theory is then defined by choosing a specific set of Hamiltonian perturbations, which amounts to deforming the given admissible Lagrangians so that their phases are in increasing order, and ignoring boundary intersections.

EVk and pushing forward their product by integration along the fibers of evo. This setup allows us to "smudge" incidence conditions by replacing the integration current on a submanifold Ci by a smooth differential form supported in a tubular neighborhood. Given bE CPl(L, L), Fukaya-Oh-Ohta-Ono [14] deform the Aoo-algebra structure on the Floer complex by setting We will actually restrict our attention to the case where b is a cycle, representing a class [b] E Hl(L) (or, dually, in H n -l(L)). 2:0, Ai --+ +oo}.

Denote by (XV, W) the mirror to X, and by D V the mirror to D, which we identify symplectically with a fiber of W, say D V = {W = et } C XV for fixed t » O. First we need to briefly describe the Fukaya category of the LandauGinzburg model W : XV -t C. The general idea, which goes back to Kontsevich [27] and Hori-Iqbal-Vafa [22], is to allow as objects admissible Lagrangian submanifolds of Xv; these can be described either as potentially non-compact Lagrangian submanifolds which, outside of a compact subset, are invariant under the gradient flow of -Re(W), or, truncating, as compact Lagrangian submanifolds with (possibly empty) boundary contained inside a fixed reference fiber of W (and satisfying an additional condition).

Download PDF sample

Surveys in Differential Geometry (Volume 13): Geometry, Analysis and Algebraic Geometry by various, Huai-Dong Cao (Lehigh University), Shing-Tung Yau (Harvard University)


by Edward
4.5

Rated 4.96 of 5 – based on 6 votes