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arXiv:math.GT/0403102v15Mar2004 AN INVOLUTION ACTING NONTRIVIALLY ON
 

Summary: arXiv:math.GT/0403102v15Mar2004
AN INVOLUTION ACTING NONTRIVIALLY ON
HEEGARD-FLOER HOMOLOGY
SELMAN AKBULUT AND SELAHI DURUSOY
Abstract. We show that a certain involution on a homology sphere induces a
nontrivial homomorphism on its Heegard-Floer homology groups (recently defined
by Ozsv´ath and Szab´o). We discuss application of this to constructing exotic smooth
structures on 4-manifolds.
0. Introduction
Let W be the smooth contractible 4-manifold consisting of a single 1- and 2- handle
attached as in Figure 1 (one of the Mazur manifolds).
0
W
Figure 1.
The boundary is a homology sphere = W. Let f : be the obvious
involution obtained by first surgering S1
× B3
to B2
× S2
in the interior of W, then

  

Source: Akbulut, Selman - Department of Mathematics, Michigan State University

 

Collections: Mathematics