scholarly journals A note on the topological transversality theorem for the admissible maps of Gorniewicz

2019 ◽  
Vol 12 (06) ◽  
pp. 345-348 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Transversality Theorem ◽  
Admissible Maps

On a Converse of Kneser's Transversality Theorem

1935 ◽  
Vol 36 (3) ◽  
pp. 749 ◽  
Author(s):  
Lincoln LaPaz ◽  
Tibor Rado
Keyword(s):  
Transversality Theorem

scholarly journals A Topological Coincidence Theory for Multifunctions via Homotopy

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 427
Author(s):  
Donal O’Regan
Keyword(s):  
Simple Result ◽  
Coincidence Theory ◽  
Transversality Theorem

A new simple result is presented which immediately yields the topological transversality theorem for coincidences.

Maps between p-completed classifying spaces

1989 ◽  
Vol 112 (3-4) ◽  
pp. 231-235 ◽  
Author(s):  
J. Frank Adams ◽  
Zdzisław Wojtkowiak
Keyword(s):  
Lie Groups ◽  
Classifying Spaces ◽  
Compact Lie Groups ◽  
Complete Case ◽  
Topological Map ◽  
Maximal Tori ◽  
Local Case ◽  
Admissible Maps

SynopsisLet G and G' be two connected compact Lie groups with maximal tori T and T'. For a space X, let Xp be the p-completion of X. We will associate to each topological map f:(BG)p→(BG')p an “admissible map” ϕ:π1(T)⊗zZp→π1(T′)⊗zZp. We then show that the study of “admissible maps” in the p-complete case may be reduced to their study in the p-local case.

Some results on positive eigenvalues of admissible maps

2003 ◽  
Vol 52 (7) ◽  
pp. 1755-1763 ◽  
Author(s):  
In-Sook Kim
Keyword(s):  
Admissible Maps

scholarly journals GENERALIZED TWISTS AS ELASTIC ENERGY EXTREMALS ON ANNULI, QUATERNIONS AND LIFTING TWIST LOOPS TO THE SPINOR GROUPS

2013 ◽  
Vol 11 (02) ◽  
pp. 1350008 ◽  
Author(s):  
M. S. SHAHROKHI-DEHKORDI ◽  
A. TAHERI
Keyword(s):  
Elastic Energy ◽  
Lagrange Equation ◽  
Energy Functional ◽  
Double Cover ◽  
Explicit Representation ◽  
Exponential Map ◽  
Dirichlet Energy ◽  
Smooth Solutions ◽  
Low Dimensions ◽  
Admissible Maps

Let X = {x ∈ ℝn : a < |x| < b} be a generalized annulus and consider the Dirichlet energy functional [Formula: see text] over the space of admissible maps [Formula: see text] where φ is the identity map. In this paper we consider a class of maps referred to as generalized twists and examine them in connection with the Euler–Lagrange equation associated with 𝔽[⋅, X] on [Formula: see text]. The approach is novel and is based on lifting twist loops from SO(n) to its double cover Spin(n) and reformulating the equations accordingly. We restrict our attention to low dimensions and prove that for n = 4 the system admits infinitely many smooth solutions in the form of twists while for n = 3 this number sharply reduces to one. We discuss some qualitative features of these solutions in view of their remarkable explicit representation through the exponential map of Spin(n).

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