A homological selection theorem implying a division theorem for Q-manifolds

• Autorzy: Taras Banakh , Robert Cauty
• Języki publikacji: EN

Abstrakty

EN

We prove that a space M with Disjoint Disk Property is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. This implies that the product M × I² of a space M with the disk is a Q-manifold if and only if M × X is a Q-manifold for some C-space X. The proof of these theorems exploits the homological characterization of Q-manifolds due to Daverman and Walsh, combined with the existence of G-stable points in C-spaces. To establish the existence of such points we prove (and afterward apply) homological versions of the Brouwer Fixed Point Theorem and of Uspenskij's Selection Theorem.

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 57N75: General position and transversality
• 55N10: Singular theory
• 57N20: Topology of infinite-dimensional manifolds
• 54H25: Fixed-point and coincidence theorems
• 54C65: Selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2007
• Tom: 77
• Numer: 1
• Strony: 11-22

Daty

wydano

2007

Twórcy

autor

Taras Banakh

• Instytut Matematyki, Akademia Świętokrzyska, Kielce, Poland
• Department of Mathematics, Ivan Franko Lviv National University, Lviv, Ukraine
• Nipissing University, North Bay, Canada

autor

Robert Cauty

• Université Paris VI, France

Identyfikatory

DOI

10.4064/bc77-0-1