The Arf-Kervaire problem in algebraic topology: an introduction
نویسندگان
چکیده
منابع مشابه
The Arf-kervaire Invariant Problem in Algebraic Topology: Introduction
This paper gives the history and background of one of the oldest problems in algebraic topology, along with a short summary of our solution to it and a description of some of the tools we use. More details of the proof are provided in our second paper in this volume, The Arf-Kervaire invariant problem in algebraic topology: Sketch of the proof. A rigorous account can be found in our preprint Th...
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We provide a sketch of the proof of the non-existence of Kervaire Invariant one manifolds using equivariant homotopy theory [15]. A treatment of the statement and history of the problem can be found in “The Arf-Kervaire problem in algebraic topology: Introduction”. Our goal here is to introduce the reader to the techniques used to prove the result and to familiarize them with the kinds of compu...
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This paper gives the history and background of one of the oldest problems in algebraic topology, along with an outline of our solution to it. A rigorous account can be found in our preprint [HHR]. The third author has a website with numerous links to related papers and talks we have given on the subject since announcing our result in April, 2009.
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1 The main point of this talk The main point of this talk The 3-primary Arf-Kervaire invariant problem is still open. We have a program for solving it similar to what we did for p = 2. We are missing a crucial ingredient. Defining the problem The Arf-Kervaire invariant problem for a prime p is to determine the fate of the elements θ j = h 2 j for p = 2 b j−1 for p > 2 ∈ Ext 2,2p j (p−1) A (Z/p,...
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We gave a series of four lectures, the first by the second author and the rest by the first author. The latter was followed by a 2 hour question and answer session. The problem in question is nearly 50 years old and began with Kervaire’s paper [Ker60] of 1960 in which he defined a Z/2-valued invariant φ(M) on certain manifolds M of dimension 4m + 2. He showed that for m = 2 and M aclosed smooth...
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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 2009
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.2009.v2009.n1.a2