7,863 research outputs found
Topological triviality of smoothly knotted surfaces in 4-manifolds
Some generalizations and variations of the Fintushel-Stern rim surgery are
known to produce smoothly knotted surfaces. We show that if the fundamental
groups of their complements are cyclic, then these surfaces are topologically
unknotted. Using a twist-spinning construction from high-dimensional knot
theory, we construct examples of knotted surfaces whose complements have cyclic
fundamental groups.Comment: Final version; appeared in AMS Transactions. 15 pages, 2 figure
Double point surgery and configurations of surfaces
We introduce a new operation, double point surgery, on immersed surfaces in a
4-manifold, and use it to construct knotted configurations of surfaces in many
4-manifolds. Taking branched covers, we produce smoothly exotic actions of Z/m
x Z/n on simply connected 4-manifolds with complicated fixed-point sets.Comment: Final version; to appear in Journal of Topology. Removed assertion
about the restriction of the Z/m x Z/n action to the Z/m and Z/n subgroup
Multilevel Network Games
We consider a multilevel network game, where nodes can improve their
communication costs by connecting to a high-speed network. The nodes are
connected by a static network and each node can decide individually to become a
gateway to the high-speed network. The goal of a node is to minimize its
private costs, i.e., the sum (SUM-game) or maximum (MAX-game) of communication
distances from to all other nodes plus a fixed price if it
decides to be a gateway. Between gateways the communication distance is ,
and gateways also improve other nodes' distances by behaving as shortcuts. For
the SUM-game, we show that for , the price of anarchy is
and in this range equilibria always exist. In range
the price of anarchy is , and
for it is constant. For the MAX-game, we show that the
price of anarchy is either , for ,
or else . Given a graph with girth of at least , equilibria always
exist. Concerning the dynamics, both the SUM-game and the MAX-game are not
potential games. For the SUM-game, we even show that it is not weakly acyclic.Comment: An extended abstract of this paper has been accepted for publication
in the proceedings of the 10th International Conference on Web and Internet
Economics (WINE
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