Coincidence theorems for involutions

✍ Scribed by Jan M. Aarts; Robbert J. Fokkink; Hans Vermeer

• Book ID: 104295290
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 348 KB
• Volume: 85
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00136-3

✦ Synopsis

SEepin

(1974)

and Izydorek and Jaworowski (1995, 1996) showed that for each k and 7~ such that 2k > n there exists a contractible k-dimensional simplicial complex Y and a continuous map cp : $" -+ Y without the antipodal coincidence property, i.e., q(z) # p( -XT) for all z E 9". On the other hand, if 2k < n then every map cp : S" + Y to a k-dimensional simplicial complex has an antipodal coincidence point. In this paper it is shown that, with some minor modifications, these results remain valid when S" and the antipodal map are replaced by any normal space and an involution with color number n + 2. 0 1998 Elsevier Science B.V.