15 citations · 43 across the 6 of their papers we have counts for
18 papers · 1 filter
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…
Zeros of closed 1-forms, homoclinic orbits, and Lusternik - Schnirelman theory
Michael Farber
In this paper we study topological lower bounds on the number of zeros of closed 1-forms without Morse type assumptions. We prove that one may always find a representing closed 1-f…
Periodic trajectories in 3-dimensional convex billiards
Michael Farber, Serge Tabachnikov
We give lower bound on the number of periodic billiard trajectories inside a generic smooth strictly convex closed surface in 3-space: for odd n, there are at least 2(n-1) such tra…
Novikov - Shubin signatures, II
Michael Farber
This paper continues math.DG/9903140. Here we construct a linking form on the torsion part of middle dimensional extended L^2 homology and cohomology of odd-dimensional manifolds.…
Topology of billiard problems, I
M. Farber
Let be a strictly convex domain bounded by a smooth hypersurface . In this paper we find lower bounds on the number of billiard trajectories in $T…
Topology of cyclic configuration spaces and periodic trajectories of multi-dimensional billiards
Michael Farber, Serge Tabachnikov
We give lowed bounds on the number of periodic trajectories in strictly convex smooth billiards in for . For plane billiards (when m=1) such bounds were obtained…