Premium
Simply connected asymmetric manifolds
Author(s) -
Kreck Matthias
Publication year - 2009
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/jtopol/jtp008
Subject(s) - mathematics , simply connected space , reversing , group action , pure mathematics , congruence (geometry) , action (physics) , group (periodic table) , combinatorics , topology (electrical circuits) , geometry , physics , materials science , quantum mechanics , composite material
In this paper, we give the first examples of smooth simply connected asymmetric closed manifolds. V. Puppe has shown that there are examples of simply connected 6‐manifolds on which there is no orientation‐preserving nontrivial group action of a finite group. We show that all of them are actually asymmetric manifolds. The main tool in the proof is a congruence of a twisted A ^ ‐genus for certain Spin‐manifolds admitting an orientation‐reversing involution. This is the first restriction of this type coming from an action of a discrete group.