Open Access

Coincidence theory for spaces which fiber over a nilmanifold

Fixed Point Theory and Applications20042004:986365

DOI: 10.1155/S1687182004308107

Received: 20 August 2003

Published: 7 June 2004

Abstract

Let https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq1_HTML.gif be a finite connected complex and https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq2_HTML.gif a fibration over a compact nilmanifold https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq3_HTML.gif . For any finite complex https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq4_HTML.gif and maps https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq5_HTML.gif , we show that the Nielsen coincidence number https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq6_HTML.gif vanishes if the Reidemeister coincidence number https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq7_HTML.gif is infinite. If, in addition, https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq8_HTML.gif is a compact manifold and https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq9_HTML.gif is the constant map at a point https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq10_HTML.gif , then https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq11_HTML.gif is deformable to a map https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq12_HTML.gif such that https://static-content.springer.com/image/art%3A10.1155%2FS1687182004308107/MediaObjects/13663_2003_Article_938_IEq13_HTML.gif .

Authors’ Affiliations

(1)
Department of Mathematics, Bates College

Copyright

© Wong 2004