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A
finite-dimensional approach to the strong Novikov
conjecture
Daniel Ramras, Rufus Willett and Guoliang Yu |
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Algebraic & Geometric Topology 13 (2013) 2283–2316
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Abstract |
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The aim of this paper is to describe an approach to the (strong) Novikov conjecture based on continuous families of finite-dimensional representations: this is partly inspired by ideas of Lusztig related to the Atiyah–Singer families index theorem, and partly by Carlsson’s deformation –theory. Using this approach, we give new proofs of the strong Novikov conjecture in several interesting cases, including crystallographic groups and surface groups. The method presented here is relatively accessible compared with other proofs of the Novikov conjecture, and also yields some information about the –theory and cohomology of representation spaces. |
Keywords
Baum–Connes conjecture, $K$–homology, deformation
$K$–theory, index theory
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Mathematical Subject Classification 2010
Primary: 19K56, 19L99, 55N15, 57R20
Secondary: 20C99, 46L80, 46L85
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References |
Publication
Received: 18 October 2012
Revised: 29 January 2013
Accepted: 19 March 2013
Published: 20 June 2013
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Authors |
| Daniel Ramras | |
| Department of Mathematical
Sciences New Mexico State University Las Cruces, NM 88003 USA |
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| http://www.math.nmsu.edu/~ramras/ | |
| Rufus Willett | |
| Department of Mathematics University of Hawai‘i at Mānoa Honolulu, HI 96822 USA |
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| Guoliang Yu | |
| Department of Mathematics Texas A&M University College Station, TX 77843-3368 USA and Shanghai Center for Mathematical Sciences Fudan University Shanghai China |
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