L^2-cohomology of locally symmetric spaces, I
| dc.creator | Saper, Leslie | |
| dc.date | 2004-12-20 | |
| dc.date | 2006-01-11 | |
| dc.date.accessioned | 2026-07-07T06:39:11Z | |
| dc.date.available | 2026-07-07T06:39:11Z | |
| dc.description | Let X be a locally symmetric space associated to a reductive algebraic group G defined over Q. L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of X; they were introduced in [math.RT/0112251]. That paper also introduced the micro-support of an L-module, a combinatorial invariant that to a great extent characterizes the cohomology of the associated sheaf. The theory has been successfully applied to solve a number of problems concerning the intersection cohomology and weighted cohomology of the reductive Borel-Serre compactification [math.RT/0112251], as well as the ordinary cohomology of X [math.RT/0112250]. In this paper we extend the theory so that it covers L^2-cohomology. In particular we construct an L-module whose cohomology is the L^2-cohomology of X and we calculate its micro-support. As an application we obtain a new proof of the conjectures of Borel and Zucker. | |
| dc.description | 40 pages, AMS-LaTeX, uses Xy-pic 3.7 package; v2: minor typos fixed, minor improvements in exposition, treatment in 10.4 of homotopy in neighborhoods corrected and simplified (requiring small changes throughout section 10), section 13 expanded; v3: minor typos fixed, corrected statement of Theorem 1 | |
| dc.identifier | https://arxiv.org/abs/math/0412353 | |
| dc.identifier | http://arxiv.org/abs/math/0412353 | |
| dc.identifier | Pure Appl. Math. Q. 1 (2005), no. 4, 889-937 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100985 | |
| dc.subject | Representation Theory | |
| dc.subject | Differential Geometry | |
| dc.subject | 11F75, 22E40, 32S60, 55N33 (Primary) 14G35, 22E45 (Secondary) | |
| dc.title | L^2-cohomology of locally symmetric spaces, I | |
| dc.type | text |