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The Lusternik–Schnirelmann category of a connected sum

Volume 251 / 2020

Alexander Dranishnikov, Rustam Sadykov Fundamenta Mathematicae 251 (2020), 317-328 MSC: Primary 55M30; Secondary 57R19. DOI: 10.4064/fm792-1-2020 Published online: 5 June 2020


We use the Berstein–Hilton invariant to prove the formula $\operatorname{cat} (M\mathbin {\sharp } N)=\max \{\operatorname{cat} M, \operatorname{cat} N\}$ for the Lusternik–Schnirelmann category of the connected sum of closed manifolds $M$ and $N$.


  • Alexander DranishnikovDepartment of Mathematics
    University of Florida
    358 Little Hall
    Gainesville, FL 32611-8105, U.S.A.
  • Rustam SadykovMathematics Department
    Kansas State University
    138 Cardwell Hall
    Manhattan, KS 66506, U.S.A.

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