# Surgery Applications to a Generalized Rudyak Conjecture

@inproceedings{Scott2021SurgeryAT, title={Surgery Applications to a Generalized Rudyak Conjecture}, author={Jamie Scott}, year={2021} }

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.

- Mathematics
- 2020

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 inequality… Expand

Maps of Degree 1 and Lusternik--Schnirelmann Category

- Mathematics
- 2016

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 and… Expand

The Lusternik–Schnirelmann category of a connected sum

- Mathematics
- 2019

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 $M_1$ and… Expand

ON CATEGORY WEIGHT AND ITS APPLICATIONS

- Mathematics
- 1999

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

- Mathematics
- Proceedings of the American Mathematical Society
- 2019

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 the… Expand

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

- Mathematics
- 1972

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 Main… Expand

Surgery on compact manifolds

- Mathematics
- 1970

Preliminaries: Note on conventions Basic homotopy notions Surgery below the middle dimension Appendix: Applications Simple Poincare complexes The main theorem: Statement of results An important… Expand

On higher analogs of topological complexity

- Mathematics
- 2009

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 ( X… Expand

Topological Complexity of wedges

- Physics, Mathematics
- 2017

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 $X\vee Y$.