Abstract
We derive new vanishing theorems for genera under almost nonnegative Ricci curvature and infinite fundamental group. A vanishing theorem of Euler characteristic number for almost nonnegatively curved Alexandrov spaces is also proved.
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Acknowledgements
The authors are grateful to the anonymous referee for their careful reading and suggestions, which significantly improved the clarity of the paper. Xiaoyang Chen is partially supported by 23JC1403600 (Project title: On the topology of almost nonnegatively curved manifolds) and NSFC 12171364. He thanks Professor Botong Wang for helpful discussions. Fei Han is partially supported by the grant AcRF A-8000451-00-00 from National University of Singapore. Jian Ge is partially supported by National Key R &D Program of China grant 2020YFA0712800, NSFC 12371049 and the Fundamental Research Funds for the Central Universities.
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Chen, X., Ge, J. & Han, F. Almost nonnegative Ricci curvature and new vanishing theorems for genera. Math. Z. 306, 44 (2024). https://doi.org/10.1007/s00209-024-03448-1
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DOI: https://doi.org/10.1007/s00209-024-03448-1