homotopy groups [hō′mäd·ə·pē ‚grüps] (mathematics) Associated to a topological spaceX,the groups appearing for each positive integern,which reflect the number of different ways (up to homotopy) than ann-dimensional sphere may be mapped toX. ...
Our\nresults depend on the study of the o-minimal fundamental groupoid of G.A. BerarducciM. MaminoOn the homotopy type of definable groups in an o-minimal structure. Eprint arXiv:math.LO/0905.1069v2 - Berarducci, Mamino - 2009
Harmonic spinors and metrics of positive curvature via the Gromoll filtration and Toda brackets We construct non-trivial elements of order 2 in the homotopy groups $\\pi_{8j+1+*} Diff(D^6,\\partial)$, for * congruent 1 or 2 modulo 8, which are detecte......
HOMOTOPY GROUPS OF TRIADS W. S. MASSEY 1. Introduction. One of the most important problems of topology today is to devise methods for computing the homotopy groups of topological spaces. The present paper is an attack on one phase of this general problem. One method of attacking the problem...
On the derived categories of coherent sheaves on some homogeneous spaces Invent. Math., 92 (3) (1988), pp. 479–508 [10] Yu. Manin Quantum Groups and Noncommutative Geometry Publ. du CRM, Univ. de Montreal (1988) [11] E. Matlis Injective modules over noetherian rings Pacific J. Math...
Press, Cambridge, MA (1995) 167–201 MR1358617 Geometry & Topology Monographs 13 (2008) Homotopy algebra of open–closed strings 257 [21] W M Goldman, J J Millson, The deformation theory of representations of fundamental groups of compact Ka¨hler manifolds, Inst. Hautes E´ tudes Sci. ...
Of course, if we want to check it is an exact sequence of groups (at least, for n≥1n≥1), we need to check that the maps are all homomorphic. There are some theory on it, but is too much for this post. Cofibrations An important concept in algebraic topology is cofibration. You...
1. Introduction THE object of this note is to prove that the space BU is a direct factor of the space Q (CP)= Oto5eo (CP00)= HmQn/Sn (CPto). This is not very n surprising, as Toda [cf.(6)(2.1)] has shown that the homotopy groups of^(CP00... G Segal - 《Quarterly Jou...
spheres, homotopy groups of die 配边.然而,这个序列的第一项的明确的计算还有内在的困难,该困难还未被克服. 111.计算的结果.具有i一陀(2的群二。(S”)同构于上表中的群: 2)具有12簇k(22的群武同构于下表中的群:上料耘栩粼赫粉 关于群兀,(夕)的计算的更进一步的结果,见〔3]在这些群中的奇准素...
We will say that a finite spectrumXisevenif the homology groupsH_k (X;\mathbb{Z})are free abelian groups, which vanish whenkis odd. Equivalently, a finite spectrumXis even if it is homotopy equivalent to a finite spectrum only has even-dimensional cells. ...