Corpus ID: 237532333

Surgery Applications to a Generalized Rudyak Conjecture

@inproceedings{Scott2021SurgeryAT,
  title={Surgery Applications to a Generalized Rudyak Conjecture},
  author={Jamie Scott},
  year={2021}
}
  • Jamie Scott
  • Published 16 September 2021
  • Mathematics
Rudyak’s conjecture states that cat (M) ≥ cat (N) given a degree one map f : M → N between closed manifolds. We generalize this conjecture to sectional category, and follow the methodology of [5] to get the following result: Theorem 0.1. Consider the following commutative diagram: 

References

SHOWING 1-10 OF 18 REFERENCES
Surgery Approach to Rudyak's Conjecture.
Using the surgery we prove the following: THEOREM. Let $f:M \to N$ be a normal map of degree one between closed manifolds with $N$ being $(r-1)$-connected, $r\ge 1$. If $N$ satisfies the inequalityExpand
Maps of Degree 1 and Lusternik--Schnirelmann Category
Given a map $f: M \to N$ of degree 1 of closed manifolds. Is it true that the Lusternik--Schnirelmann category of the range of the map is not more that the category of the domain? We discuss this andExpand
The Lusternik–Schnirelmann category of a connected sum
We use the Berstein-Hilton invariant to prove the formula $\cat(M_1\sharp M_2)=\max\{\cat M_1, \cat M_2\}$ for the Lustrnik-Schnirelmann category of the connected sum of closed manifolds $M_1$ andExpand
ON CATEGORY WEIGHT AND ITS APPLICATIONS
Abstract We develop and apply the concept of category weight which was introduced by Fadell and Husseini. For example, we prove that category weight of every Massey product 〈u 1 , …, u n 〉, u i ∈ H ∗Expand
On the LS-category and topological complexity of a connected sum
The Lusternik-Schnirelmann category and topological complexity are important invariants of manifolds (and more generally, topological spaces). We study the behavior of these invariants under theExpand
Algebraic Topology
The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.
Surgery on Simply-Connected Manifolds
I. Poincare Duality.- 1. Slant Operations, Cup and Cap Products.- 2. Poincare Duality.- 3. Poincare Pairs and Triads Sums of Poincare Pairs and Maps.- 4. The Spivak Normal Fibre Space.- II. The MainExpand
Surgery on compact manifolds
Preliminaries: Note on conventions Basic homotopy notions Surgery below the middle dimension Appendix: Applications Simple Poincare complexes The main theorem: Statement of results An importantExpand
On higher analogs of topological complexity
Abstract Farber introduced a notion of topological complexity TC ( X ) that is related to robotics. Here we introduce a series of numerical invariants TC n ( X ) , n = 2 , 3 , …  , such that TC 2 ( XExpand
Topological Complexity of wedges
We prove the formula \begin{equation*} TC(X\vee Y)=\max\{TC(X),TC(Y),cat(X\times Y)\} \end{equation*} for the topological complexity of the wedge $X\vee Y$.
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