Papers › Strongly isospectral hyperbolic 3-manifolds with nonisomorphic rational cohomology rings
Strongly isospectral hyperbolic 3-manifolds with nonisomorphic rational cohomology rings
Anda Tenie
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This paper shows that one cannot "hear" the rational cohomology ring of a hyperbolic 3-manifold. More precisely, while it is well-known that strongly isospectral manifolds have the same cohomology as vector spaces, we give an example of compact hyperbolic 3-manifolds that are strongly isospectral but have nonisomorphic rational cohomology rings. Along the way we implement a computer program which finds the nullity of the cup product map H¹(M;ℚ)∧H¹(M;ℚ)→H²(M;ℚ) for any aspherical space in terms of the presentation of the fundamental group.
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