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47
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 55 (28 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 22 (3 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 "Generalized Homot ..."
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Cited by 18 (2 self)
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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 "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 15 (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 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 10 (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
On analytical applications of stable homotopy (the Arnold conjecture, critical points
 Math. Zeitschrift
, 1999
"... Abstract. We prove the Arnold conjecture for closed symplectic manifolds with π2(M) = 0 and cat M = dim M. Furthermore, we prove an analog of the Lusternik– Schnirelmann theorem for functions with “generalized hyperbolicity ” property. ..."
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Cited by 8 (0 self)
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Abstract. We prove the Arnold conjecture for closed symplectic manifolds with π2(M) = 0 and cat M = dim M. Furthermore, we prove an analog of the Lusternik– Schnirelmann theorem for functions with “generalized hyperbolicity ” property.
Mod 2 Cohomology of Combinatorial Grassmannians
"... this paper we explore the relationship between combinatorial vector bundles and real vector bundles. As a consequence of our results we get theorems relating the topology of the combinatorial Grassmannians to that of their real analogs. The theory of oriented matroids gives a combinatorial abstract ..."
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Cited by 6 (3 self)
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this paper we explore the relationship between combinatorial vector bundles and real vector bundles. As a consequence of our results we get theorems relating the topology of the combinatorial Grassmannians to that of their real analogs. The theory of oriented matroids gives a combinatorial abstraction of linear algebra; a kdimensional subspace of R