Lower bounds for the L.-S. category of products
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- by Barry Jessup and Bitjong Ndombol PDF
- Proc. Amer. Math. Soc. 117 (1993), 839-842 Request permission
Abstract:
Halperin and Lemaire introduced L.-S. category type invariants ${\text {left-}}\operatorname {Mcat} (A)$ and ${\text {right-}}\operatorname {Mcat} (A)$(/l) for certain differential algebras $(A,d)$. In particular, they proved that if $(A,d) = {C^{\ast }}(S,k)$ is the $k$-valued singular cochains on $1$-connected space $S$, then these invariants are lower bounds for the classical category ${\text {cat}}(S)$. We use an explicit model for Ganea’s space due to Felix, Halperin, Lemaire, and Thomas to prove $\operatorname {lMcat} (A \otimes B) \leqslant \operatorname {lMcat} (A) + e(B)$, over any field, where $e$ denotes Toomer’s invariant. This proves Ganea’s conjecture for Mcat over fields of arbitrary characteristic.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 839-842
- MSC: Primary 55P50; Secondary 55M30, 55P60, 55P62
- DOI: https://doi.org/10.1090/S0002-9939-1993-1152985-2
- MathSciNet review: 1152985