675 research outputs found
Fixed point data of finite groups acting on 3-manifolds
We consider fully effective orientation-preserving smooth actions of a given
finite group G on smooth, closed, oriented 3-manifolds M. We investigate the
relations that necessarily hold between the numbers of fixed points of various
non-cyclic subgroups. In Section 2, we show that all such relations are in fact
equations mod 2, and we explain how the number of independent equations yields
information concerning low-dimensional equivariant cobordism groups. Moreover,
we restate a theorem of A. Szucs asserting that under the conditions imposed on
a smooth action of G on M as above, the number of G-orbits of points x in M
with non-cyclic stabilizer G_x is even, and we prove the result by using
arguments of G. Moussong. In Sections 3 and 4, we determine all the equations
for non-cyclic subgroups G of SO(3).Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-24.abs.htm
Simply-connected 4-manifolds with a given boundary
AbstractLet M be a closed, oriented, connected 3-manifold and let (Zn,L) be a symmetric bilinear form which presents Hā(M;Z). Lt VL(M) be the set of all oriented homeomorphism types of compact, 1-connected, oriented 4-manifolds with boundary M and intersection pairing isomorphic to (Zn, L). We will give a complete description of the sets VL(M)
Collective Choice under Dichotomous Preferences
Agents partition deterministic outcomes into good or bad. A direct revelation mechanism selects a lottery over outcomes - also interpreted as time-shares. Under such dichotomous preferences, the probability that the lottery outcome be a good one is a canonical utility representation. The utilitarian mechanism averages over all deterministic outcomes "approved" by the largest number of agents. It is efficient, strategy-proof and treats equally agents and outcomes. We reach the impossibility frontier if we also place the lower bound 1/n on each agent's utility, where n is the number of agents; or if this lower bound is the fraction of good outcomes to feasible outcomes. We conjecture that no ex-ante efficient and strategy-proof mechanism guarantees a strictly positive utility to all agents at all profiles, and prove a weaker version of this conjecture.
A Novel Symmetric Four Dimensional Polytope Found Using Optimization Strategies Inspired by Thomson's Problem of Charges on a Sphere
Inspired by, and using methods of optimization derived from classical three
dimensional electrostatics, we note a novel beautiful symmetric four
dimensional polytope we have found with 80 vertices. We also describe how the
method used to find this symmetric polytope, and related methods can
potentially be used to find good examples for the kissing and packing problems
in D dimensions
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