6 citations · 13 across the 19 of their papers we have counts for
20 papers
(Injective) hom-complexity between graphs
Cesar A. Ipanaque Zapata, Josué A. Aguirre Enciso, Wilman Francisco Cuba Ramos
We present the notion of hom-complexity, , for two graphs and , along with basic results for this numerical invariant. This invariant is a num…
Sectional number of a morphism
Cesar A. Ipanaque Zapata
The genus of a fibration was introduced by Schwarz in 1962. Given a continuous map , the usual sectional number is the least integer~ such that c…
Relative sectional number and the coincidence property
Cesar A. Ipanaque Zapata, Felipe A. Torres Estrella
For a Hausdorff space , a topological space and a map , we present a connection between the relative sectional number of the first coordinate projection $π_{2,1}^Y…
The Injective category number on continuous maps
Cesar A. Ipanaque Zapata, Roland Rabanal
We introduce the concept of injective category number for a continuous map , and present fundamental results concerning this numerical invariant. The…
Sectional Category and the parametrized Borsuk-Ulam property
Cesar A. Ipanaque Zapata, Daciberg L. Gonçalves
In this paper, for fibrations , over and a free involution which satisfy the equality , we discover a connection between the sectio…
Topological complexity of Milnor fibration
Cesar A. Ipanaque Zapata, Taciana O. Souza
In this paper we discover a connection between the Milnor fibration theory and current research trends in topological robotics. The configuration space and workspace are often desc…
Index and Sectional Category
Cesar Augusto Ipanaque Zapata, Daciberg Lima Gonçalves
Let be a finite group with order and . For a free -space , we introduce a notion of -th index of , denoted by .…
Transversal motion planning
Cesar A. Ipanaque Zapata, Fernando R. Chu Rivera
In this paper, we introduce the notion of transversal topological complexity (TTC) for a smooth manifold with respect to a submanifold of codimension 1 together with basic resu…
Higher topological complexity of a map
Cesar A. Ipanaque Zapata, Jesús González
The higher topological complexity of a space , , , and the topological complexity of a map , , have been introduced by Rudyak and…
Borsuk-Ulam property and Sectional Category
Cesar A. Ipanaque Zapata, Daciberg L. Gonçalves
For a Hausdorff space , a free involution and a Hausdorff space , we discover a connection between the sectional category of the double covers and $q^…
On the topology of the Milnor fibration
Taciana O. Souza, Cesar A. Ipanaque Zapata
In this paper we present new results about the topology of the Milnor fibrations of analytic function-germs with a special attention to the topology of the fibers. In particular, w…
Sectional category and The Fixed Point Property
Cesar A. Ipanaque Zapata, Jesús González
For a Hausdorff space , we exhibit an unexpected connection between the sectional number of the Fadell-Neuwirth fibration , and the fixed point property (…
Collision-free spatial motion of rigid bodies via topological complexity
Cesar A. Ipanaque Zapata
The Topological complexity a la Farber is a homotopy invariant which have interesting applications in Robotics, specifically, in the robot motion planning problem. I…
Cross-sections of Milnor fibrations and Motion planning
Cesar A. I. Zapata
Consider a fibration \[p:E\to S^{p-1}\] with fiber . We have the following natural question: Under what conditions does this fibration admit a cross-section? Our purpose is to d…
Multitasking collision-free motion planning algorithms in Euclidean spaces
Cesar A. Ipanaque Zapata, Jesus Gonzalez
We present optimal motion planning algorithms which can be used in designing practical systems controlling objects moving in Euclidean space without collisions. Our algorithms are…
Topological Complexity of wedges
Cesar A. Ipanaque Zapata
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 .
Category and Topological Complexity of the configuration space
Cesar A. Ipanaque Zapata
The Lusternik-Schnirelmann category cat and topological complexity TC are related homotopy invariants. The topological complexity TC has applications to the robot motion planning p…
Collision-free motion planning on manifolds with boundary
Cesar A. Ipanaque Zapata
This paper concerns the study of the homotopy type of the ordered configuration space for manifolds with boundary and as an application we will study the collision free motion plan…
Non-contractible configuration spaces
Cesar Augusto Ipanaque Zapata
Let be the configuration space of ordered tuples of distinct points in the manifold . Using the Fadell-Neuwirth fibration, we prove that the configuration spaces $F…
Lusternik-Schnirelmann category of the configuration space of complex projective space
Cesar A. Ipanaque Zapata
The Lusternik-Schnirelmann category is a homotopy invariant which is a numerical bound on the number of critical points of a smooth function on a manifold. Another similar…