L 2-Cohomology and Intersection Cohomology of Certain Arithmetic Varieties

Armand Borel
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Armand Borel: Institute for Advanced Study, School of Mathematics

A chapter in Emmy Noether in Bryn Mawr, 1983, pp 119-131 from Springer

Abstract: Abstract L 2-cohomology of non-compact manifolds and intersection cohomology are two fairly recent topics. In principle, they are independent from one another, one belonging to differential geometry or analysis, the other to algebraic topology and algebraic geometry. However, some interesting relations between the two appeared almost from the beginning. To what extent they are special cases of rather general phenomena is not known at present, but, for a number of people, the evidence is tantalizing enough to make it appear worthwhile to try to investigate this further. From a broader point of view, one can view this as an attempt to add a new chapter to a topic with an already long history: the connections between differential geometry and topology or, more specifically, the representation of topological invariants by means of analytical objects.

Keywords: Hodge Structure; Arithmetic Group; Intersection Cohomology; Intersection Homology; Poincare Duality (search for similar items in EconPapers)
Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-5547-5_8

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DOI: 10.1007/978-1-4612-5547-5_8

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