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Minimizing Coincidence Numbers of Maps into Projective Spaces
, 2008
"... In this paper we continue to study (“strong”) Nielsen coincidence numbers (which were introduced recently for pairs of maps between manifolds of arbitrary dimensions) and the corresponding minimum numbers of coincidence points and pathcomponents. We explore compatibilities with fibrations and, more ..."
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In this paper we continue to study (“strong”) Nielsen coincidence numbers (which were introduced recently for pairs of maps between manifolds of arbitrary dimensions) and the corresponding minimum numbers of coincidence points and pathcomponents. We explore compatibilities with fibrations and, more specifically, with covering maps, paying special attention to selfcoincidence questions. As a sample application we calculate each of these numbers for all maps from spheres to (real, complex, or quaternionic) projective spaces. Our results turn out to be intimately related to recent work of D. Gonçalves and D. Randall concerning maps which can be deformed away from themselves but not by small deformations; in particular, there are close connections to the
Selfcoincidences and roots in Nielsen theory
"... Abstract. Given two maps f1 and f2 from the sphere S m to an nmanifold N, when are they loose, i.e. when can they be deformed away from one another? We study the geometry of their (generic) coincidence locus and its Nielsen decomposition. On one hand the resulting bordism class of coincidence data ..."
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Abstract. Given two maps f1 and f2 from the sphere S m to an nmanifold N, when are they loose, i.e. when can they be deformed away from one another? We study the geometry of their (generic) coincidence locus and its Nielsen decomposition. On one hand the resulting bordism class of coincidence data and the corresponding Nielsen numbers are strong looseness obstructions. On the other hand the values which these invariants may possibly assume turn out to satisfy severe restrictions, e.g. the Nielsen numbers can only take the values 0, 1 or the cardinality of the fundamental group of N. In order to show this we compare different Nielsen classes in the root case (where f1 or f2 is constant) and we use the fact that all but possibly one Nielsen class are inessential in the selfcoincidence case (where f1 = f2). Also we deduce strong vanishing results.
DOI: 10.2140/gtm.2008.14.193 · Source: arXiv CITATIONS
, 2009
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
JIANGTYPE THEOREMS FOR COINCIDENCES OF MAPS INTO HOMOGENEOUS SPACES
"... Abstract. Let f, g: X → G/K be maps from a closed connected orientable manifold X to an orientable coset space M = G/K where G is a compact connected Lie group, K a closed subgroup and dimX = dimM. In this paper, we show that if L(f, g) = 0 ..."
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Abstract. Let f, g: X → G/K be maps from a closed connected orientable manifold X to an orientable coset space M = G/K where G is a compact connected Lie group, K a closed subgroup and dimX = dimM. In this paper, we show that if L(f, g) = 0