Mimar Sinan Güzel Sanatlar Üniversitesi Matematik Bölümü Genel Seminerleri<br><br>Arf-Kervaire Invariant Problem<br>Konuşmacı: Prof. Dr. Turgut Önder (Ortadoğu Teknik Üniversitesi)<br><br>Yer : 408 No’lu Amfi<br>
MSGSÜ Fen Edebiyat Fakültesi (Beşiktaş)<br>
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Zaman : 6 Kasım 2009 Cuma, 11:00<br>
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Not: Konuşma İngilizce olacaktır.<br><br>Öz:<br>Arf-Kervaire invariant is an invariant of an n-dimensional framed differentiable manifold for n=4k+2. It is the Arf invariant of a certain quadratic form on the (2k+1)-dimensional homology group of the manifold with the coefficient group integers modulo 2, and it takes the values 0 or 1.<br>
<br>The problem of determining the dimensions n in which there are n-dimensional framed manifolds of Arf-Kervaire invariant 1 is called the Arf-Kervaire invariant problem. It is the key to several important problems in algebraic and geometric topology, for instance the classification problems of higher dimensional manifolds. On 21 April 2009 Michael Hopkins, Douglas Ravenel and Michael Hill announced that they have completed the solution of this 45-year-old problem except for the dimension n=126. On 26 August 2009 they have published a 99 pages preprint in the arXive explaining the details of the proof.<br>
<br>In this talk we shall outline for a general audience the Arf-Kervaire invariant problem and the developments leading to its solution.<br><br>