1. CJM 2012 (vol 65 pp. 553)
|Addendum and Erratum to "The Fundamental Group of $S^1$-manifolds"|
This paper provides an addendum and erratum to L. Godinho and M. E. Sousa-Dias, "The Fundamental Group of $S^1$-manifolds". Canad. J. Math. 62(2010), no. 5, 1082--1098.
Keywords:symplectic reduction; fundamental group
Categories:53D19, 37J10, 55Q05
2. CJM 2010 (vol 62 pp. 1082)
|The Fundamental Group of $S^1$-manifolds|
We address the problem of computing the fundamental group of a symplectic $S^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a Hamiltonian $S^1$-action. Several examples are presented to illustrate our main results.
Categories:53D20, 37J10, 55Q05
3. CJM 2009 (vol 62 pp. 284)
|Self-Maps of Low Rank Lie Groups at Odd Primes|
Let G be a simple, compact, simply-connected Lie group localized at an odd prime~p. We study the group of homotopy classes of self-maps $[G,G]$ when the rank of G is low and in certain cases describe the set of homotopy classes of multiplicative self-maps $H[G,G]$. The low rank condition gives G certain structural properties which make calculations accessible. Several examples and applications are given.
Keywords:Lie group, self-map, H-map
Categories:55P45, 55Q05, 57T20
4. CJM 1998 (vol 50 pp. 342)
|Shape fibrations, multivalued maps and shape groups |
The notion of shape fibration with the near lifting of near multivalued paths property is studied. The relation of these maps---which agree with shape fibrations having totally disconnected fibers---with Hurewicz fibrations with the unique path lifting property is completely settled. Some results concerning homotopy and shape groups are presented for shape fibrations with the near lifting of near multivalued paths property. It is shown that for this class of shape fibrations the existence of liftings of a fine multivalued map, is equivalent to an algebraic problem relative to the homotopy, shape or strong shape groups associated.
Keywords:Shape fibration, multivalued map, homotopy groups, shape, groups, strong shape groups
Categories:54C56, 55P55, 55Q05, 55Q07, 55R05