Reflections on closed manifolds

✍ Scribed by Ricardo N. Cruz

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 773 KB
• Volume: 87
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00166-1

✦ Synopsis

A local reflection T: hl + 121, Af a closed and connected manifold, is an involution with a two-sided fixed point submanifold F (in particular, nonempty). We show that /&o(F) < g(kJ) + I, g(A4) the genus of hl (Cornea, 1989). We also show that /&(N -F) < 2. If @"(hi -F) = 2 we call T a reflection. In this case we prove that T is conjugate to the reflection that exchanges the two copies of M/T in nr/r = Al/r Ua Al/r,. In particular, A1 is a double. Further results are obtained. These involutions arise in Dynamical Systems (