M. Davis, 2-primary v1-periodic homotopy groups of SU (n), Amer. J. Math. 114 (1991) 465-494, MR 93g:55018.M. Bendersky and D. M. Davis, The v1-periodic homotopy groups of SO(n), to appear in Memoirs AMS. http://www.lehigh.edu/∼dmd1/son.htmlM. Bendersky and D. M...
Homotopy groups were first studied systematically by Witold Hurewicz in [30] and [31]. DEFINITION 3.1.1 The n-th homotopy group of X, πn(X) is the set of homotopy classes of maps from the n-sphere Sn (the space of unit vectors in Rn+1) to X which send a fixed point in Sn (...
For $n\\geq 2$, the homotopy groups $\\pi_n(S^2)$ are non-zero.doi:10.4310/HHA.2016.v18.n2.a18Sergei O. IvanovRoman MikhailovJie WuHomology, Homotopy and ApplicationsS. Ivanov, R. Mikhailov, J. Wu, On nontriviality of homotopy groups of spheres, http://arxiv.org/abs/1506.00952...
Although the latter is a more intuitive concept, the former will prove to be more interesting: it will allow for the introduction of a group structure. This paper describes the history of the concept of homotopy of paths and its after-effects in, e.g., higher homotopy groups. View chapter...
The ν1-Periodic Homotopy Groups of SU(n) at Odd Primes These groups can be extended to smaller (and negative) values of k by periodicity, if desired. The v 1 -periodic homotopy groups of the symplectic groups Sp(m) can also be read off from this result.Reviewer: M.Mimura (Okayama)...
The geometry with ordinary basic groups is called simply connected. The calculation of basic groups involves more in-depth details, such as the specific definition of topology, mapping between topological Spaces, etc., which cannot be explained in detail here. For friends who are interested in ...
n ,suchasmanifolds, cell-complexes. •Inalgebraictopology,wealsolookatmappingspaces, namelythespaceofallcontinuousmapsfromaspaceX toaspaceY. SpacesHomotopyClassificationProblemHomotopyGroups •Theusual(andmostinteresting)topologicalspacesare subspacesofEuclideanspacesR ...
In this paper, we consider the homotopy types of gauge groups of principal SO(4)- bundles over S4. Our results are stated in more generality. Let Z be a subgroup of (S3)n generated by an element (−1, . . . , −1). Define Kn = (S3)n/Z . Then, in particular, K1 = SO...
Then we have the following diagram of sets: (I n , ∂I n ) f //(X, x 0 ) (I n /∂I n , ∂I n /∂I n ) g 66 Now we have (I n /∂I n , ∂I n /∂I n ) (S n , s 0 ). So we can also define ...
Dochtermann, A.: Homotopy groups of hom complexes of graphs. J. Combin. Theory Ser. A 116(1), 180–194 (2009) Article MathSciNet Google Scholar Droz, J.M.: Quillen model structures on the category of graphs. Homology Homotopy Appl. 14(2), 265–284 (2012) Article MathSciNet Googl...