1,341 research outputs found
The modular geometry of Random Regge Triangulations
We show that the introduction of triangulations with variable connectivity
and fluctuating egde-lengths (Random Regge Triangulations) allows for a
relatively simple and direct analyisis of the modular properties of 2
dimensional simplicial quantum gravity. In particular, we discuss in detail an
explicit bijection between the space of possible random Regge triangulations
(of given genus g and with N vertices) and a suitable decorated version of the
(compactified) moduli space of genus g Riemann surfaces with N punctures. Such
an analysis allows us to associate a Weil-Petersson metric with the set of
random Regge triangulations and prove that the corresponding volume provides
the dynamical triangulation partition function for pure gravity.Comment: 36 pages corrected typos, enhanced introductio
Parity sheaves on the affine Grassmannian and the Mirkovi\'c-Vilonen conjecture
We prove the Mirkovi\'c-Vilonen conjecture: the integral local intersection
cohomology groups of spherical Schubert varieties on the affine Grassmannian
have no p-torsion, as long as p is outside a certain small and explicitly given
set of prime numbers. (Juteau has exhibited counterexamples when p is a bad
prime.) The main idea is to convert this topological question into an algebraic
question about perverse-coherent sheaves on the dual nilpotent cone using the
Juteau-Mautner-Williamson theory of parity sheaves.Comment: 27 pages. v4: added details to Section 2 and an appendix on sheaf
functors on non-locally compact space
Algebraic functions and closed braids
This article was originally published in Topology 22 (1983). The present
hyperTeXed redaction includes references to post-1983 results as Addenda, and
corrects a few typographical errors. (See math.GT/0411115 for a more
comprehensive overview of the subject as it appears 21 years later.)Comment: 12 pages, 2 figure
Configuration Spaces of Manifolds with Boundary
We study ordered configuration spaces of compact manifolds with boundary. We
show that for a large class of such manifolds, the real homotopy type of the
configuration spaces only depends on the real homotopy type of the pair
consisting of the manifold and its boundary. We moreover describe explicit real
models of these configuration spaces using three different approaches. We do
this by adapting previous constructions for configuration spaces of closed
manifolds which relied on Kontsevich's proof of the formality of the little
disks operads. We also prove that our models are compatible with the richer
structure of configuration spaces, respectively a module over the Swiss-Cheese
operad, a module over the associative algebra of configurations in a collar
around the boundary of the manifold, and a module over the little disks operad.Comment: 107 page
- …