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A History of the Arf-Kervaire Invariant Problem
A History of the Arf-Kervaire. Invariant Problem. Victor P. Snaith. “I know what you' re thinking about,” said. Tweedledum; “but it isn't so, nohow.” “Con- trariwise ...

This paper gives the history and background of one of the oldest problems ... in this volume, The Arf-Kervaire invariant problem in algebraic topology: Sketch of ...

The Kervaire invariant - Harvard Mathematics Department
Feb 24, 2012 ... The Kervaire invariant problem is a fundamental problem in stable ... introduce the Kervaire invariant, describe the history of the Kervaire ...

The Arf-Kervaire invariant of framed manifolds - Mathematics
mental unresolved problem in homotopy theory which has a history extending ... I had recently published a monograph on the Arf-Kervaire invariant [101].

The Kervaire invariant in homotopy theory - Northwestern University
See [12]. Parallel to this geometric story, the Kervaire invariant problem also arose in ... Suppose Sn is the sphere of origin of α and a is a class in πn+kSn which.

The Kervaire invariant problem?
Mar 25, 2016 ... The history and solution of the Kervaire invariant problem is ... Keywords and phrases: Kervaire invariant, framed manifold, homotopy groups of ...

Chapter 7 Hurewicz Images, BP-theory and the Arf-Kervaire Invariant
2.3 Applications to the Arf-Kervaire invariant one problem . . . . . . . 44 .... This basic unsolved problem has a history extending back over fifty years. Inspection of ...

arXiv:math/9801123v1 [math.AG] 27 Jan 1998
Feb 1, 2008 ... ∗A chapter for the book “History of Topology”, ed I. M. James. †Author ... ogy have entered singularity theory, where algebraic problems have been .... invariants of the link of a curve singularity becomes increasingly messy as. 6 .... bundle to Sn. The Kervaire sphere may or may not be diffeomorphic to.

on this syllabus - MIT Mathematics
Jan 16, 2016 ... Historical introduction, to be given by Hill or Ravenel. The Kervaire invariant problem originated with the work of Kervaire-Milnor [KM63] (and.

Michel Kervaire work on knots in higher dimensions
Sep 2, 2014 ... results of Hill-Hopkins-Ravenel on the Kervaire Invariant Problem and its ... The point of view adopted in this paper is kind of pseudo-historical.

Groups of homotopy spheres, surgery, and the Kervaire invariant
GROUPS OF HOMOTOPY SPHERES, SURGERY, AND THE KERVAIRE .... and the rest is history. We get a ... There are two related arf-invariant problems going.

Research Statement - MIT Mathematics
Oct 31, 2016 ... solution to the Kervaire invariant one problem by Hill, Hopkins and ..... 3Of course this approach is backwards compared to the historical ...

Mark Mahowald - MIT Mathematics
not attempt an exhaustive survey of the relevant history of homotopy theory; for more information .... This spectral sequence effectively broke the problem .... jecture by saying that the stable Hopf invariant of a class of Kervaire invariant one is a ...

Algebraic Topology Background - Springer
Stable Homotopy Around the Arf-Kervaire Invariant ... 1 deals with the history of the calculations of stable homotopy groups of spheres (the ... Finally § 8 describes several equivalent formulations of the Arf-Kervaire invariant one problem.

Topological spherical space forms
Dec 28, 2014 ... The existence and classification problems for space forms have a long history in the geometry and topology of manifolds. ...... Cobordism invariants, the Kervaire invariant and fixed point free involutions, Trans. Amer. Math. Soc ...

A survey of applications of surgery to knot and link theory. - Brandeis
In dimension one, the manifold embedding problem is knot and link theory. This article attempts a ... We proceed, largely, from an historical perspective .... boundary and signature or Kervaire invariant a given element a ∈ Pn+1. Then d( a) is.

Surveys on Surgery Theory Volume 2 - University of Chicago
history and bibliography of surgery would have been a very complicated ..... invariants (for example, the Pontrjagin classes) of the two manifolds M1 and M2 can ...... the “Kervaire problem” (a simply connected surgery problem representing.
wall2, surveys in surgery.pdf

The ENIAC - School of Mathematics & Statistics - University College
Sep 26, 2013 ... Size of the Problem. Cometary motion is a relatively simple problem, .... A History of the Arf-Kervaire Invariant. Problem page 1040. Cover of the ...

For printing - MSP
Nov 29, 2006 ... An important problem in global Riemannian geometry is that of ... and Tuschmann [37]) for a discussion of the history and pertinent references. In [13; ..... the Arf invariant and † is the Kervaire sphere, ie, the generator of bP2nI.

Review (Jahresbericht der DMV): Modern Classical Homotopy
The subject has a long history starting around 1950 (with some important earlier ... An important recent result is the solution of the Kervaire invariant problem by Hill, Hopkins and Ravenel. The original problem is a question about smooth.

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