Coincidence Nielsen numbers for covering maps for orientable and nonorientable manifolds

Moh'D, Fida (2008) Coincidence Nielsen numbers for covering maps for orientable and nonorientable manifolds. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

Let f, g : M → N be maps between closed manifolds of the same dimension, and let p : M → M and p' : N → N be finite regular covering maps. If the manifolds M and N are orientable, then, under certain conditions, the Nielsen number N (f,g) of f and g can be computed as a linear combination of the Nielsen numbers of the lifts of f and g. In the non-orientable case, using semi-index, we introduce two new Nielsen numbers. The first one is the Linear Nielsen number NL (f,g), which is a linear combination of the Nielsen numbers of the lifts of f and g. The second one is the Non-linear Nielsen number NED (f,g). It is the number of certain essential classes whose inverse images by p are inessential Nielsen classes. In fact, N (f,g) = NL (f,g) + NED (f,g), where by abuse of notation, N (f,g) denotes the coincidence Nielsen number defined using semi-index.

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