Fixed points of n-valued maps on surfaces and the Wecken property-a configuration space approach

作者：Goncalves Daciberg Lima^*; Guaschi John

来源：Science China Mathematics, 2017, 60(9): 1561-1574.

DOI：10.1007/s11425-017-9080-x

• multivalued maps
• fixed points
• Wecken property
• Nielsen numbers
• braids
• configuration space

In this paper, we explore the fixed point theory of n-valued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane (resp. the 2-sphere S-2) has the Wecken property for n-valued maps for all n a a"center dot (resp. all n 3). In the case n = 2 and S-2, we prove a partial result about the Wecken property. We then describe the Nielsen number of a non-split n-valued map of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q: XI, -> X with a subset of the coordinate maps of a lift of the n-valued split map phi circle q: (X) over cap-circle X.

• 出版日期2017-9