Results 21 to 30 of about 330 (59)
An easily verifiable proof of the Brouwer fixed point theorem [PDF]
, 2011 We give a remarkably elementary proof of the Brouwer fixed point theorem.
Suzuki, Tomonari, Takeuchi, Yukio
core +2 more sources
A Hadwiger Theorem for Simplicial Maps [PDF]
, 2014 We define the notion of valuation on simplicial maps between geometric realizations of simplicial complexes in $\mathbb{R}^n$. Valuations on simplicial maps are analogous to valuations on sets.
Matthew L. Wright +2 more
core
Orbit spaces of free involutions on the product of two projective spaces
, 2010 Let $X$ be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on $X$ and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the Leray ...
A. Borel +18 more
core +1 more source
The Lefschetz-Hopf theorem and axioms for the Lefschetz number
, 2004 The reduced Lefschetz number, that is, the Lefschetz number minus 1, is proved to be the unique integer-valued function L on selfmaps of compact polyhedra which is constant on homotopy classes such that (1) L(fg) = L(gf), for f:X -->Y and g:Y -->X; (2 ...
Arkowitz, Martin, Brown, Robert F.
core +4 more sources
Cohomology of preimages with local coefficients
, 2006 Let M,N and B\subset N be compact smooth manifolds of dimensions n+k,n and \ell, respectively. Given a map f from M to N, we give homological conditions under which g^{-1}(B) has nontrivial cohomology (with local coefficients) for any map g homotopic to ...
Daccach +10 more
core +2 more sources
Parametrized Borsuk-Ulam problem for projective space bundles
, 2010 Let $\pi: E \to B$ be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let $\pi^{'}: E^{'} \to B$ be vector bundle such that $\mathbb{Z}_2$ acts fiber preserving and freely on $E$ and $E^{'}-0 ...
Singh, Mahender
core +1 more source
Knaster's problem for $(Z_2)^k$-symmetric subsets of the sphere $S^{2^k-1}$
, 2009 We prove a Knaster-type result for orbits of the group $(Z_2)^k$ in $S^{2^k-1}$, calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew crosspolytopes in hypersurfaces in $\mathbb R^{2^k}$, and a result about ...
A. Borel +28 more
core +2 more sources
A Discrete Multivariate Mean Value Theorem with Applications [PDF]
AMS classifications: 47H10; 54H25; 55M20; 90C33; 91B50Discrete set;mean value theorem;fixed point;algorithm;equilibrium ...
Talman, A.J.J., Yang, Z.F.
core +1 more source
Minimizing coincidence numbers of maps into projective spaces
, 2008 In this paper we continue to study (`strong') Nielsen coincidence numbers (which were introduced recently for pairs of maps between manifolds of arbitrary dimensions) and the corresponding minimum numbers of coincidence points and pathcomponents.
Koschorke, Ulrich
core +1 more source
A formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles [PDF]
, 2007 We give a formula for the coincidence Reidemeister trace of selfmaps on bouquets of circles in terms of the Fox calculus. Our formula reduces the problem of computing the coincidence Reidemeister trace to the problem of distinguishing doubly twisted ...
Staecker, P. Christopher
core +4 more sources