15 citations · 73 across the 18 of their papers we have counts for
5 papers · 2 filters
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…
On the zero-in-the-spectrum conjecture
M. Farber, S. Weinberger
We prove that the answer to the "zero-in-the-spectrum" conjecture, in its form, suggested by J. Lott, is negative. Namely, we show that for any n > 5 there exists a closed n-dimens…
Absolute torsion and eta-invariant
Michael Farber
In a recent joint work with V. Turaev (cf. math.DG/9810114) we defined a new concept of combinatorial torsion which we called absolute torsion. Compared with the classical Reidemei…
Novikov - Shubin signatures, I
Michael Farber
Torsion objects of von Neumann categories describe the phenomen "spectrum near zero" discovered by S. Novikov and M. Shubin. In this paper we classify Hermitian forms on torsion ob…
Counting zeros of closed 1-forms
Michael Farber
The paper suggests new topological lower bounds for the number of zeros of closed 1-forms within a given cohomology class. The main new technical tool is the deformation complex, w…