12 citations · 20 across the 4 of their papers we have counts for
6 papers · 1 filter
Refined Analytic Torsion
Maxim Braverman, Thomas Kappeler
For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of…
L^2 torsion without the determinant class condition and extended L^2 cohomology
M. Braverman, A. Carey, M. Farber +1
We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatoria…
Kirwan-Novikov inequalities on a manifold with boundary
Maxim Braverman, Valentin Silantyev
We extend the Novikov Morse-type inequalities for closed 1-forms in 2 directions. First, we consider manifolds with boundary. Second, we allow a very degenerate structure of the cr…
New proof of the Cheeger-Muller Theorem
Maxim Braverman
We present a short analytic proof of the equality between the analytic and combinatorial torsion. We use the same approach as in the proof given by Burghelea, Friedlander and Kappe…
Vanishing theorems on covering manifolds
Maxim Braverman
Let be an oriented even-dimensional Riemannian manifold on which a discrete group of orientation-preserving isometries acts freely, so that the quotient is compact.…
Vanishing theorems for the kernel of a Dirac operator
Maxim Braverman
We obtain a vanishing theorem for the kernel of a Dirac operator on a Clifford module twisted by a sufficiently large power of a line bundle, whose curvature is non-degenerate at a…