TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS ABSTRACT TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS Petar Pavešić, University of Ljubljana Topological complexity of a map was initially introduced as a measure of the manipulation complexity of a mechanical device with a given forward kinematic map. The resulting concept is not homotopy invariant because kinematic maps that appear in robotics usually have singularities. On the other hand, the topological complexity of a fibration is homotopy invariant, so we may consider the approximation of the topological complexity of an arbitrary map by the topological complexity of the associated fibration. In our talk we will discuss the topological complexity of fibrations and their relation with the complexity of general maps. In particular, we will consider the important special case of covering maps and their complexity. Bedlewo - 2017 1

Review of TC(X) TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS 2

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS REVIEW OF TC(X) 3

TC of a map TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS 4

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS TC OF A MAP 5

A x TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS TC OF A MAP 6

y A TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS TC OF A MAP 7

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS INVARIANCE Invariance TC=2 TC=1 8

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS INVARIANCE 9

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS INVARIANCE 10

Cohomological estimate TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS COHOMOLOGICAL ESTIMATE Cohomological estimate 11

Fibrations dimension-connectivity estimate TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS FIBRATIONS Fibrations dimension-connectivity estimate 12

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS FIBRATIONS 13

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS FIBRATIONS 14

Coverings TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS 15

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS COVERINGS 16

TOPOLOGICAL COMPLEXITY OF FIBRATIONS AND COVERING MAPS THE END 17