80 research outputs found
Whitehead torsion of inertial h-cobordisms
We study the Whitehead torsions of inertial h-cobordisms, and identify
various types representing a nested sequence of subsets of the Whitehead group.
A number of examples are given to show that these subsets are all different in
general
Symmetries and exotic smooth structures on a surface
Smooth and symplectic symmetries of an infinite family of distinct exotic
surfaces are studied, and comparison with the corresponding symmetries of
the standard is made. The action on the lattice induced by a smooth
finite group action is shown to be strongly restricted, and as a result,
nonsmoothability of actions induced by a holomorphic automorphism of a prime
order is proved and nonexistence of smooth actions by several
groups is established (included among which is the binary tetrahedral group
which has the smallest order). Concerning symplectic symmetries, the
fixed-point set structure of a symplectic cyclic action of a prime order is explicitly determined, provided that the action is homologically
nontrivial.Comment: 46 pages, final version, Journal of Topology, to appea
How different can h-cobordant manifolds be?
We study the homeomorphism types of manifolds h-cobordant to a fixed one. Our
investigation is partly motivated by the notion of special manifolds introduced
by Milnor in his study of lens spaces. In particular we revisit and clarify
some of the claims concerning h-cobordisms of these manifolds.Comment: 16 pages. Typo corrected and reference adde
Symmetric symplectic homotopy K3 surfaces
A study on the relation between the smooth structure of a symplectic homotopy
K3 surface and its symplectic symmetries is initiated. A measurement of
exoticness of a symplectic homotopy K3 surface is introduced, and the influence
of an effective action of a K3 group via symplectic symmetries is investigated.
It is shown that an effective action by various maximal symplectic K3 groups
forces the corresponding homotopy K3 surface to be minimally exotic with
respect to our measure. (However, the standard K3 is the only known example of
such minimally exotic homotopy K3 surfaces.) The possible structure of a finite
group of symplectic symmetries of a minimally exotic homotopy K3 surface is
determined and future research directions are indicated.Comment: 30 pages, 1 figure, with a slightly changed title. Accepted for
publication by the Journal of Topolog
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