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Counting maximally broken Morse trajectories on aspherical manifolds


We prove a lower bound on the number of maximally broken trajectories of the negative gradient flow of a Morse–Smale function on a closed aspherical manifold in terms of integral (torsion) homology.

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Correspondence to Caterina Campagnolo.

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The authors acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 281869850 (RTG 2229).

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Campagnolo, C., Sauer, R. Counting maximally broken Morse trajectories on aspherical manifolds. Geom Dedicata 202, 387–399 (2019).

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  • Morse–Smale function
  • Torsion homology
  • Broken Morse trajectories
  • Simplicial norm

Mathematics Subject Classification (2010)

  • Primary 57R99
  • Secondary 55N10