SOBRE PONTOS FIXOS DE APLICAÇÕES ENTRE FIBRADOS COM FIBRA SUPERFÍCIE

Penteado, Dirceu

doi:10.11606/T.55.2019.tde-08042019-160435

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Doctoral Thesis

DOI

https://doi.org/10.11606/T.55.2019.tde-08042019-160435

Document

Doctoral Thesis

Author

Penteado, Dirceu (Catálogo USP)

Full name

Dirceu Penteado

Institute/School/College

Instituto de Ciências Matemáticas e de Computação

Knowledge Area

Geometry and Topology

Date of Defense

1988-06-30

Published

São Carlos, 1988

Supervisor

Goncalves, Daciberg Lima (Catálogo USP)

Committee

Goncalves, Daciberg Lima (President)
Hacon, Derek Douglas Jack
Manzoli Neto, Oziride
Randall, Alwyn Duane
Rigas, Alcibiades

Title in Portuguese

SOBRE PONTOS FIXOS DE APLICAÇÕES ENTRE FIBRADOS COM FIBRA SUPERFÍCIE

Keywords in Portuguese

Não disponível

Abstract in Portuguese

Não disponível

Title in English

Not available

Keywords in English

Not availabe

Abstract in English

Let p:E → B be locally trivial fibre space with fibre F, where F, E, B are connected compact manifolds (without boundary). Let f : E → E be a fibre preserving map inducing 1_{B>/sub> : B → B. E. Fadell and S. Husseini in [FaBO] studied the question of deform a map f to fixed pointfree map (f.p.f.)by fibrewise homotopy. They show that the problem is equivalent to lift the map (1, f)) : E → E x_B E through the inclusionh i : E x_BE-δ → E x_b E. There they consider the homotopy fibre F_B of the inclusion i. They assume that dim F = n ≥ 3 so they can use obstruction theory with local coefficient ∏_n-1 (F_B) wihich is abelian. In this work we study the case where F is a torus. We consider the local coefficient system on E determined by H₁(F_b) and we can defined the obstruction abelianized D (1, f) ∈ H² (E; {H₁ (F_B)}) . We compute D (1, f) in some examples when p : E → B is principal torus fibered bundle. In this case, we defined a number i(f) ∈ N. Geometrically i(f) is minimun number of the connected componnent of fix(g), where g = f by fiberwise homotopy. In case that F is torus and B = S¹, we also estabelish necessary and sufficient conditions to deform f to f.p.f map by fiberwise homotpy.}

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Publishing Date

2019-04-08

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