**Contemporary Mathematics**

Volume: 702;
2018;
176 pp;
Softcover

MSC: Primary 55; 20; 52; 57; 68; 93;

**Print ISBN: 978-1-4704-3436-6
Product Code: CONM/702**

List Price: $117.00

AMS Member Price: $93.60

MAA Member Price: $105.30

**Electronic ISBN: 978-1-4704-4405-1
Product Code: CONM/702.E**

List Price: $117.00

AMS Member Price: $93.60

MAA Member Price: $105.30

# Topological Complexity and Related Topics

Share this page *Edited by *
*Mark Grant; Gregory Lupton; Lucile Vandembroucq*

This volume contains the proceedings of the mini-workshop on
Topological Complexity and Related Topics, held from February
28–March 5, 2016, at the Mathematisches Forschungsinstitut
Oberwolfach.

Topological complexity is a numerical homotopy invariant, defined
by Farber in the early twenty-first century as part of a topological
approach to the motion planning problem in robotics. It continues to
be the subject of intensive research by homotopy theorists, partly due
to its potential applicability, and partly due to its close
relationship to more classical invariants, such as the
Lusternik–Schnirelmann category and the Schwarz genus.

This volume contains survey articles and original research papers
on topological complexity and its many generalizations and variants,
to give a snapshot of contemporary research on this exciting topic at
the interface of pure mathematics and engineering.

#### Readership

Graduate students and research mathematicians interested in algebraic topology and its applications, applications of pure mathematics to engineering, and engineers interested in topology and the motion planning problem.

# Table of Contents

## Topological Complexity and Related Topics

- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- Equivariant topological complexities 110
- Rational methods applied to sectional category and topological complexity 1726
- Introduction 1827
- 1. Sullivan’s rational homotopy theory 1928
- 2. Rational Lusternik-Schnirelmann category 2837
- 3. The Whitehead and Ganea characterizations 3140
- 4. Rational approximations of sectional category 3241
- 5. Characterization à la Félix-Halperin 3443
- 6. A mapping theorem for topological complexity 3847
- Acknowledgements 3948
- References 3948

- Topological complexity of classical configuration spaces and related objects 4150
- A topologist’s view of kinematic maps and manipulation complexity 6170
- On the cohomology classes of planar polygon spaces 8594
- Sectional category of a class of maps 91100
- Q-topological complexity 103112
- Topological complexity of graphic arrangements 121130
- Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes 133142
- Topological complexity of collision-free multi-tasking motion planning on orientable surfaces 151160
- Topological complexity of subgroups of Artin’s braid groups 165174
- Back Cover Back Cover1186