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92
The type of the classifying space for a family of subgroups
 J. Pure Appl. Algebra
"... We define for a topological group G and a family of subgroupsF two versions for the classifying space for the family F, the GCWversion EF(G) and the numerable Gspace version JF(G). They agree if G is discrete, or if G is a Lie group and each element inF compact, or ifF is the family of compact su ..."
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Cited by 109 (31 self)
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We define for a topological group G and a family of subgroupsF two versions for the classifying space for the family F, the GCWversion EF(G) and the numerable Gspace version JF(G). They agree if G is discrete, or if G is a Lie group and each element inF compact, or ifF is the family of compact subgroups. We discuss special geometric models for these spaces for the family of compact open groups in special cases such as almost connected groups G and word hyperbolic groups G. We deal with the question whether there are finite models, models of finite type, finite dimensional models. We also discuss the relevance of these spaces for the BaumConnes Conjecture about the topological Ktheory of the reduced group C ∗algebra, for the FarrellJones Conjecture about the algebraic Kand Ltheory of group rings, for Completion Theorems and for classifying spaces for equivariant vector bundles and for other situations.
A PARAMETRIZED INDEX THEOREM FOR THE ALGEBRAIC KTHEORY EULER CLASS
, 1995
"... RiemannRoch theorems assert that certain algebraically defined wrong way maps (transfers) in algebraic K–theory agree with topologically defined ones [BaDo]. Bismut and Lott [BiLo] proved such a Riemann–Roch theorem where the wrong way maps are induced by the projection of a smooth fiber bundle, an ..."
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Cited by 44 (6 self)
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RiemannRoch theorems assert that certain algebraically defined wrong way maps (transfers) in algebraic K–theory agree with topologically defined ones [BaDo]. Bismut and Lott [BiLo] proved such a Riemann–Roch theorem where the wrong way maps are induced by the projection of a smooth fiber bundle, and the topologically defined transfer map is the Becker–Gottlieb transfer. We generalize and refine their theorem, and prove a converse stating that the Riemann–Roch condition is equivalent to the existence of a fiberwise smooth structure. In the process, we prove a family index theorem where the K–theory used is algebraic K–theory, and the fiber bundles have topological (not necessarily smooth) manifolds as fibers.
Homotopy colimits  comparison lemmas for combinatorial applications
, 1997
"... We provide a "toolkit " of basic lemmas for the comparison of homotopy types of homotopy colimits of diagrams of spaces over small categories. We show how this toolkit can be used on quite different fields of applications. We demonstrate this with respect to 1. Bjorner's " ..."
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Cited by 24 (2 self)
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We provide a &quot;toolkit &quot; of basic lemmas for the comparison of homotopy types of homotopy colimits of diagrams of spaces over small categories. We show how this toolkit can be used on quite different fields of applications. We demonstrate this with respect to 1. Bjorner's "Generalized Homotopy Complementation Formula" [4], 2. the topology of toric varieties, 3. the study of homotopy types of arrangements of subspaces, 4. the analysis of homotopy types of subgroup complexes.
Generators for the Cohomology Ring of the Moduli Space of Rank 2 Higgs Bundles
 Proc. London Math. Soc. 88 (2004) 632–658, arXiv: math.AG/0003093. T. Hausel, N. Proudfoot / Topology 44
, 2002
"... This paper will show that, in the rank 2 case, the cohomology ring of this noncompact space is again generated by universal classes. A companion paper [23] gives a complete set of explicit relations between these generators ..."
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Cited by 24 (6 self)
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This paper will show that, in the rank 2 case, the cohomology ring of this noncompact space is again generated by universal classes. A companion paper [23] gives a complete set of explicit relations between these generators
On the universal space for group actions with compact isotropy
 In Geometry and topology: Aarhus
, 1998
"... Let G be a locally compact topological group and EG its universal space for the family of compact subgroups. We give criteria for this space to be Ghomotopy equivalent to a ddimensional GCWcomplex, a finite GCWcomplex or a GCWcomplex of finite type. Essentially we reduce these questions to d ..."
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Cited by 23 (4 self)
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Let G be a locally compact topological group and EG its universal space for the family of compact subgroups. We give criteria for this space to be Ghomotopy equivalent to a ddimensional GCWcomplex, a finite GCWcomplex or a GCWcomplex of finite type. Essentially we reduce these questions to discrete groups, and to the homological algebra of the orbit category of discrete groups with respect to certain families of subgroups. Key words: universal space of a group for a family, topological group 1991 mathematics subject classification: 55R35
T.Rybicki, On the Group of Diffeomorphisms Preserving a Locally Conformal Symplectic Structure
 Ann. Global Anal. and Geom
, 1999
"... Abstract. The automorphism group of a locally conformal symplectic structure is studied. It is shown that this group possesses essential features of the symplectomorphism group. By using a special type of cohomology the flux and Calabi homomorphisms are introduced. The main theorem states that the ..."
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Cited by 19 (4 self)
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Abstract. The automorphism group of a locally conformal symplectic structure is studied. It is shown that this group possesses essential features of the symplectomorphism group. By using a special type of cohomology the flux and Calabi homomorphisms are introduced. The main theorem states that the kernels of these homomorphisms are simple groups, for the precise statement see chapter 7. Some of the methods used, may also be interesting in the symplectic case.
On Yetter’s invariant and an extension of the DijkgraafWitten invariant to categorical groups
 Theory Appl. Categ
"... We give an interpretation of Yetter’s Invariant of manifolds M in terms of the homotopy type of the function space TOP(M,B(G)), where G is a crossed module and B(G) is its classifying space. From this formulation, there follows that Yetter’s invariant depends only on the homotopy type of M, and the ..."
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Cited by 15 (0 self)
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We give an interpretation of Yetter’s Invariant of manifolds M in terms of the homotopy type of the function space TOP(M,B(G)), where G is a crossed module and B(G) is its classifying space. From this formulation, there follows that Yetter’s invariant depends only on the homotopy type of M, and the weak homotopy type of the crossed module G. We use this interpretation to define a twisting of Yetter’s Invariant by cohomology classes of crossed modules, defined
From Minimal Geodesics to Supersymmetric Field Theories
"... In memory of Raoul Bott, friend and mentor. Abstract. There are many models for the Ktheory spectrum known today, each one having its own history and applications. The purpose of this note is to give an elementary description of eight such models (and certain completions of them) and to relate all ..."
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Cited by 12 (3 self)
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In memory of Raoul Bott, friend and mentor. Abstract. There are many models for the Ktheory spectrum known today, each one having its own history and applications. The purpose of this note is to give an elementary description of eight such models (and certain completions of them) and to relate all of them by canonical maps, some of which are homeomorphisms (rather than just homotopy equivalences). Our survey begins with Raoul Bott’s iterated spaces of minimal geodesics in orthogonal groups, whichheusedtoprovehisfamousperiodicity theorem, and includes Milnor’s spaces of Clifford module structures as well as the Atyiah – Singer spaces of Fredholm operators. From these classical descriptions we move via spaces of unbounded operators and supersemigroups of operators to our most recent model, which is given by certain spaces of supersymmetric (11)dimensional field theories. These spaces were introduced by the second two authors for the purpose of generalizing them to spaces of certain supersymmetric (21)dimensional Euclidean field theories that are conjectured to be related to the Hopkins – Miller spectrum TMF of topological modular forms.