Coincidence theory for spaces which fiber over a nilmanifold

• Main Author: Wong Peter
• Format: Article
• Language: English
• Published: SpringerOpen 2004-01-01
• Series: Fixed Point Theory and Applications
• Online Access: http://www.fixedpointtheoryandapplications.com/content/2004/986365

<p/> <p>Let <inline-formula><graphic file="1687-1812-2004-986365-i1.gif"/></inline-formula> be a finite connected complex and <inline-formula><graphic file="1687-1812-2004-986365-i2.gif"/></inline-formula> a fibration over a compact nilmanifold <inline-formula><graphic file="1687-1812-2004-986365-i3.gif"/></inline-formula>. For any finite complex <inline-formula><graphic file="1687-1812-2004-986365-i4.gif"/></inline-formula> and maps <inline-formula><graphic file="1687-1812-2004-986365-i5.gif"/></inline-formula>, we show that the Nielsen coincidence number <inline-formula><graphic file="1687-1812-2004-986365-i6.gif"/></inline-formula> vanishes if the Reidemeister coincidence number <inline-formula><graphic file="1687-1812-2004-986365-i7.gif"/></inline-formula> is infinite. If, in addition, <inline-formula><graphic file="1687-1812-2004-986365-i8.gif"/></inline-formula> is a compact manifold and <inline-formula><graphic file="1687-1812-2004-986365-i9.gif"/></inline-formula> is the constant map at a point <inline-formula><graphic file="1687-1812-2004-986365-i10.gif"/></inline-formula>, then <inline-formula><graphic file="1687-1812-2004-986365-i11.gif"/></inline-formula> is deformable to a map <inline-formula><graphic file="1687-1812-2004-986365-i12.gif"/></inline-formula> such that <inline-formula><graphic file="1687-1812-2004-986365-i13.gif"/></inline-formula>.</p>