Z₂-coefficient homology (1, 2)-systolic freedom of RP³ # RP³
Chen, Lizhi
Original · EN
We prove the 3-manifold ³ # ³ is of ₂-coefficient homology (1, 2)-systolic freedom. Given a Riemannian metric on ³# ³, we define ₂-coefficient homology 1-systole as the infimum of lengths of all nonseparating geodesic loops representing nontrivial classes in H₁(³#³; ₂). The ₂-coefficient homology 2-systole is defined to be the infimum of areas of all nonseparating surfaces representing nontrivial classes in H₂(³#³; ₂). In the paper we show that there exists a sequence of Riemannian metrics on ³ # ³ such that the volume of ³ # ³ cannot be bounded below in terms of the product of ₂-coefficient homology 1-systole and ₂-coefficient homology 2-systole.
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