Year: 2026
Type: article
Abstract: Let $$F\hookrightarrow M{\mathop {\rightarrow }\limits ^{q\,}}M/F$$ F ↪ M → q M / F be a fibration, where M is a compact Lie group, $$F\subset M$$ F ⊂ M is a closed subgroup and M / F is the homogeneous space of left cosets. Let W be an orientable, connected, closed manifold of the same dimension as M . Given maps $$f,g:W\rightarrow M/F$$ f , g : W → M / F that lift through q , we establish a comparison between the ranks of the $$\check{\textrm{C}}$$ C ˇ ech cohomology groups of the fiber F and those of the coincidence set $$\textrm{Coin}(f,g)$$ Coin ( f , g ) . As a consequence, we show that for any maps $$f_1\simeq f$$ f 1 ≃ f and $$g_1\simeq g$$ g 1 ≃ g , the coincidence set $$\textrm{Coin}(f_1,g_1)$$ Coin ( f 1 , g 1 ) cannot be a proper subset of any embedded copy of F within W , unless it is empty. We then apply this result to describe minimal coincidence sets for any pairs of maps from either $$S^3$$ S 3 or $$\mathbb {R}\textrm{P}^3$$ R P 3 into either $$S^2$$ S 2 or $$\mathbb {R}\textrm{P}^2$$ R P 2
Institutions: Universidade Federal de Uberlândia, Universidade de São Paulo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7153262142