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… (More)

We use the duality between compactly supported cohomology of the associative graph complex and the cohomology of the mapping class group to show that the duals of the Kontsevich cycles [Wλ]… (More)

We prove the Witten Conjecture which says that the Miller-MoritaMumford classes for the mapping class group of punctured surfaces are dual to the Witten cycles [W2k]. The answer is exactly as… (More)

We show that exceptional sequences for hereditary algebras are characterized by the fact that the product of the corresponding reflections is the inverse Coxeter element in the Weyl group. We use… (More)

We define the notion of a "framed function" on a compact smooth manifold N and we show that the space of all framed functions on N is (dim N I)-connected. A framed function on N is essentially a… (More)

We introduce continuous Frobenius categories. These are topological categories which are constructed using representations of the circle over a discrete valuation ring. We show that they are… (More)

In standard Morse theory one usually takes a compact smooth (C) manifold M with boundary the union of three manifolds d0M ud1MuD x I where / = [0, 1], D x 0 = dd0M and D x 1 = dd1M. However for the… (More)

This paper gives a short summary of the central role played by Ed Brown’s “twisting cochains” in higher FranzReidemeister (FR) torsion and higher analytic torsion. Briefly, any fiber bundle gives a… (More)

It is known that the combinatorial classes in the cohomology of the mapping class group of punctures surfaces defined by Witten and Kontsevich are polynomials in the adjusted Miller–Morita–Mumford… (More)