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- W3199515898 abstract "Rudyak's conjecture states that cat$(M) geq$ cat$(N)$ given a degree one map $f:M to N$ between closed manifolds. We generalize this conjecture to sectional category, and follow the methodology of [5] to get the following result: Given a normal map of degree one $f:M to N$ between smooth closed manifolds, fibrations $p^M:E^M to M$ and $p^N:E^N to N$, and lift $overline{f}$ of $f$ with respect to $p^M$ and $p^N$, i.e., $fp^M = overline{f} p^N$; then if $f$ has no surgery obstructions and $N$ satisfies the inequality $5 leq dim N leq 2r$ secat$(p^N) - 3$ (where the fiber of $p^N$ is $(r-2)$-connected for some $r geq 1$), then secat$(p^M) geq$secat$(p^N)$. Finally, we apply this result to the case of higher topological complexity when $N$ is simply connected." @default.
- W3199515898 created "2021-09-27" @default.
- W3199515898 creator A5013718142 @default.
- W3199515898 date "2021-09-16" @default.
- W3199515898 modified "2023-09-27" @default.
- W3199515898 title "Surgery Applications to a Generalized Rudyak Conjecture" @default.
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