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L2-Invariants and Their Applications to Geometry, Group Theory and Spectral Theory

In: Mathematics Unlimited — 2001 and Beyond

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  • Wolfgang Lück

Abstract

During the last decades mathematics has developed at an incredible speed and a large amount of new information and results have been accumulated. Therefore mathematics faces the problem that it breaks up into different areas which may not communicate among one another. Fortunately recent developements go in the opposite direction. In particular interactions of different fields have turned out to be very fruitful and lead to new ideas and innovations. The key observation is that some of the techniques developed in one specific field can be exported to other areas and be successfully used to solve problems there. This is only possible if the techniques are so well examined and documented that they are quickly accessible to advanced mathematicians, who are not experts at the particular field, and can be understood by graduate students within a reasonable period of time.

Suggested Citation

  • Wolfgang Lück, 2001. "L2-Invariants and Their Applications to Geometry, Group Theory and Spectral Theory," Springer Books, in: Björn Engquist & Wilfried Schmid (ed.), Mathematics Unlimited — 2001 and Beyond, pages 859-871, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56478-9_42
    DOI: 10.1007/978-3-642-56478-9_42
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