相关论文: Structures of Three-Manifilds

This is a condensed exposition of the results of math.QA/0601337, based on a talk of the first author at the Oberwolfach workshop "Deformations and Contractions in Mathematics and Physics", 15-21 January 2006.

These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.

These are the notes from a series of lectures the author gave at Harvard University in the Fall of 1994. The goal of these lectures is to give a self-contained exposition of recent result of Cherednik (\cite{C6}), who proved Macdonald's…

These lecture notes explain the construction and basic properties of the wonderful compactification of a complex semisimple group of adjoint type. An appendix discusses the more general case of a semisimple symmetric space.

The notion of Poincare gauge manifold ($G$), proposed in the context of an (1+1) gravitational theory by Cangemi and Jackiw (D. Cangemi and R. Jackiw, Ann. Phys. (N.Y.) 225 (1993) 229), is explored from a geometrical point of view. First…

These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is…

We show that if $P$ is a $PD_3$-complex and $g\in\pi_1(P)$ has finite order $>1$ and infinite centraliser then $\pi_1(P)$ retracts onto $Z/2Z\oplus\mathbb{Z}$. If $P$ is an irreducible closed 3-manifold then it follows from the Projective…

In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.

This paper presents, with explanatory details, the handle decompositions, fundamental groups and homology groups of 3-manifolds, including some knot complements. Hence, along this paper, when the word manifold appears it is implicit that…

These lecture notes give a very short introduction to coarsening phenomena and summarize some recent results in the field. They focus on three aspects: the super-universality hypothesis, the geometry of growing structures, and coarsening in…

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject had been collected in author's book [Total mean curvature and sub manifolds of finite type, World Scientific, NJ, 1984]. A…

These are lecture notes for a 4h mini-course held in Toulouse, May 9-12th, at the thematic school on "Quantum topology and geometry". The goal of these lectures is to (a) explain some incarnations, in the last ten years, of the idea of…

These are the notes from my courses on the arithmetic of quadratic forms.

These are notes for a summer course given at the PIMS Summer School on Geometric and Topological Aspects of the Representation Theory of Finite Groups in Vancouver, July 27-30 2016.

This is a condensed exposition of the results of a future work, based on a talk of the second author at the Oberwolfach workshop "Poisson Geometry", April 30--4 May 2007.

These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.

In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…

This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.

This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (February 6 - 12, 2005). It gives self-contained and simplified definitions of quantum cluster algebras introduced…

This is an exposition of recent developments in the theory of bounded differences between primes. Readers are expected to be beginners of analytic number theory. The present text is a substantially improved and augmented version of the one…