scholarly journals Effectual topological complexity

2021 ◽  
pp. 1-18
Author(s):  
Natalia Cadavid-Aguilar ◽  
Jesús González ◽  
Bárbara Gutiérrez ◽  
Cesar A. Ipanaque-Zapata
Keyword(s):  
Klein Bottle ◽  
Orbit Space ◽  
Topological Complexity ◽  
Equivariant Homotopy ◽  
Hopf Invariant ◽  
Homotopy Invariant

We introduce the effectual topological complexity (ETC) of a [Formula: see text]-space [Formula: see text]. This is a [Formula: see text]-equivariant homotopy invariant sitting in between the effective topological complexity of the pair [Formula: see text] and the (regular) topological complexity of the orbit space [Formula: see text]. We study ETC for spheres and surfaces with antipodal involution, obtaining a full computation in the case of the torus. This allows us to prove the vanishing of twice the nontrivial obstruction responsible for the fact that the topological complexity of the Klein bottle is [Formula: see text]. In addition, this gives a counterexample to the possibility — suggested in Pavešić’s work on the topological complexity of a map — that ETC of [Formula: see text] would agree with Farber’s [Formula: see text] whenever the projection map [Formula: see text] is finitely sheeted. We conjecture that ETC of spheres with antipodal action recasts the Hopf invariant one problem, and describe (conjecturally optimal) effectual motion planners.

An n-dimensional Klein bottle

2019 ◽  
Vol 149 (5) ◽  
pp. 1207-1221
Author(s):  
Donald M. Davis
Keyword(s):  
Euclidean Space ◽  
Homotopy Type ◽  
Klein Bottle ◽  
Stable Homotopy ◽  
Cohomology Algebra ◽  
Topological Complexity ◽  
Integral Cohomology ◽  
Planar Polygon

AbstractAn n-dimensional analogue of the Klein bottle arose in our study of topological complexity of planar polygon spaces. We determine its integral cohomology algebra and stable homotopy type, and give an explicit immersion and embedding in Euclidean space.

scholarly journals Topological complexity of the Klein bottle

2017 ◽  
Vol 1 (2) ◽  
pp. 199-213 ◽  
Author(s):  
Daniel C. Cohen ◽  
Lucile Vandembroucq
Keyword(s):  
Klein Bottle ◽  
Topological Complexity

scholarly journals Topological complexity of the work map

2019 ◽  
pp. 1-20
Author(s):  
Aniceto Murillo ◽  
Jie Wu
Keyword(s):  
Configuration Space ◽  
Point Of View ◽  
Topological Complexity ◽  
Robot System ◽  
Homotopy Invariant ◽  
The Given

We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the task for which the system has been designed. From a purely topological point of view, this is a homotopy invariant of a map which generalizes the classical topological complexity of a space.

Electromagnetic-launch-based method for cost-efficient space debris removal

2020 ◽  
Vol 29 (1) ◽  
pp. 94-106
Author(s):  
Chongyuan Hou ◽  
Yuan Yang ◽  
Yikang Yang ◽  
Kaizhong Yang ◽  
Xiao Zhang ◽  
...  
Keyword(s):  
Space Debris ◽  
Orbit Space ◽  
Low Earth Orbit ◽  
Research Progress ◽  
Area Of Interest ◽  
Electromagnetic Launch ◽  
Debris Removal ◽  
Significant Research ◽  
Electromagnetic Launcher ◽  
Cost Efficient

AbstractThe increase in space debris orbiting Earth is a critical problem for future space missions. Space debris removal has thus become an area of interest, and significant research progress is being made in this field. However, the exorbitant cost of space debris removal missions is a major concern for commercial space companies. We therefore propose the debris removal using electromagnetic launcher (DREL) system, a ground-based electromagnetic launch system (railgun), for space debris removal missions. The DREL system has three components: a ground-based electromagnetic launcher (GEML), suborbital vehicle (SOV), and mass of micrometer-scale dust (MSD) particles. The average cost of removing a piece of low-earth orbit space debris using DREL was found to be approximately USD 160,000. The DREL method is thus shown to be economical; the total cost to remove more than 2,000 pieces of debris in a cluster was only approximately USD 400 million, compared to the millions of dollars required to remove just one or two pieces of debris using a conventional space debris removal mission. By using DREL, the cost of entering space is negligible, thereby enabling countries to remove their space debris in an affordable manner.

scholarly journals Smooth functorial field theories from B-fields and D-branes

2021 ◽  
Vol 16 (1) ◽  
pp. 75-153
Author(s):  
Severin Bunk ◽  
Konrad Waldorf
Keyword(s):  
Field Theory ◽  
Sigma Models ◽  
Lagrangian Approach ◽  
Field Theories ◽  
Open Strings ◽  
Homotopy Invariant ◽  
Target Manifold ◽  
Definition Of ◽  
Smooth Map

AbstractIn the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth open-closed functorial field theory (FFT) in the sense of Atiyah, Segal, and Stolz–Teichner. We give a detailed construction of this smooth FFT, based on the definition of a suitable smooth bordism category. In this bordism category, all manifolds are equipped with a smooth map to a spacetime target manifold. Further, the object manifolds are allowed to have boundaries; these are the endpoints of open strings stretched between D-branes. The values of our FFT are obtained from the B-field and its D-branes via transgression. Our construction generalises work of Bunke–Turner–Willerton to include open strings. At the same time, it generalises work of Moore–Segal about open-closed TQFTs to include target spaces. We provide a number of further features of our FFT: we show that it depends functorially on the B-field and the D-branes, we show that it is thin homotopy invariant, and we show that it comes equipped with a positive reflection structure in the sense of Freed–Hopkins. Finally, we describe how our construction is related to the classification of open-closed TQFTs obtained by Lauda–Pfeiffer.

Dehydration-driven evolution of topological complexity in ethylamonium uranyl selenates

2017 ◽  
Vol 247 ◽  
pp. 105-112 ◽  
Author(s):  
Vladislav V. Gurzhiy ◽  
Sergey V. Krivovichev ◽  
Ivan G. Tananaev
Keyword(s):  
Topological Complexity

scholarly journals Constructing the Graphs That Triangulate Both the Torus and the Klein Bottle

1999 ◽  
Vol 77 (1) ◽  
pp. 211-218 ◽  
Author(s):  
Serge Lawrencenko ◽  
Seiya Negami
Keyword(s):  
Klein Bottle
Sign in / Sign up

Export Citation Format

Share Document