On Kontsevich’s Characteristic Classes for Higher Dimensional Sphere Bundles Ii: Higher Classes
نویسندگان
چکیده
This paper studies Kontsevich’s characteristic classes of smooth bundles with fiber a ‘singularly’ framed odd-dimensional homology sphere which are defined through his graph complex and configuration space integral. We will give a systematic construction of smooth bundles parametrized by trivalent graphs and will show that our smooth bundles are nontrivially detected by Kontsevich’s characteristic classes. It turns out that there are many nontrivial elements of the rational homotopy groups of the diffeomorphism groups of spheres which are not in K. Igusa’s stable range. In particular, the homotopy groups of the diffeomorphism groups in some non-stable dimension range are not finite.
منابع مشابه
On Kontsevich’s Characteristic Classes for Higher Dimensional Homology Sphere Bundles and Milnor’s 0-invariant
This paper is concerned with M. Kontsevich’s universal characteristic classes of smooth bundles with fiber a ‘singularly’ framed odd-dimensional homology sphere. The main object of the present paper is to show that Kontsevich classes for fiber dimensions greater than 3 are highly non-trivial even after being made framing independent. We have two approaches: (i) explicit framing correction with ...
متن کاملOn Kontsevich’s Characteristic Classes for Smooth 5- and 7-dimensional Homology Sphere Bundles
Kontsevich constructed universal characteristic classes of smooth bundles with fiber a framed odd-dimensional homology sphere, which is known in the 3-dimensional case that they are universal among finite type invariants. The purpose of the present paper is twofold. First, we obtain a bordism invariant of smooth unframed bundles with fiber a 5dimensional homology sphere as a sum of the simplest...
متن کامل1 99 7 Mirror Principle I
Abstract. We propose and study the following Mirror Principle: certain sequences of multiplicative equivariant characteristic classes on Kontsevich’s stable map moduli spaces can be computed in terms of certain hypergeometric type classes. As applications, we compute the equivariant Euler classes of obstruction bundles induced by any concavex bundles – including any direct sum of line bundles –...
متن کاملAxioms for Higher Torsion Invariants of Smooth Bundles
We explain the relationship between various characteristic classes for smooth manifold bundles known as “higher torsion” classes. We isolate two fundamental properties that these cohomology classes may or may not have: additivity and transfer. We show that higher Franz-Reidemeister torsion and higher Miller-Morita-Mumford classes satisfy these axioms. Conversely, any characteristic class of smo...
متن کاملCharacteristic Classes of A∞-algebras
A standard combinatorial construction, due to Kontsevich, associates to any A∞-algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We propose an alternative version of this construction based on noncommutative geometry and use it to prove that homotopy equivalent algebras give rise to the same cohomology ...
متن کامل