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L 2-Cohomology and Intersection Cohomology of Certain Arithmetic Varieties

In: Emmy Noether in Bryn Mawr

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  • Armand Borel

    (Institute for Advanced Study, School of Mathematics)

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.

Suggested Citation

  • Armand Borel, 1983. "L 2-Cohomology and Intersection Cohomology of Certain Arithmetic Varieties," Springer Books, in: Bhama Srinivasan & Judith D. Sally (ed.), Emmy Noether in Bryn Mawr, pages 119-131, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5547-5_8
    DOI: 10.1007/978-1-4612-5547-5_8
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