Schick, Thomas

[["dc.bibliographiccitation.firstpage","77"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Reviews in Mathematical Physics"],["dc.bibliographiccitation.lastpage","112"],["dc.bibliographiccitation.volume","17"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Schick, Thomas"],["dc.date.accessioned","2017-09-07T11:47:11Z"],["dc.date.available","2017-09-07T11:47:11Z"],["dc.date.issued","2005"],["dc.description.abstract","We study a topological version of the T-duality relation between pairs consisting of a principal U(1)-bundle equipped with a degree-three integral cohomology class. We describe the homotopy type of a classifying space for such pairs and show that it admits a selfmap which implements a T-duality transformation. We give a simple derivation of a T-duality isomorphism for certain twisted cohomology theories. We conclude with some explicit computations of twisted K-theory groups and discuss an example of iterated T-duality for higher-dimensional torus bundles."],["dc.identifier.doi","10.1142/S0129055X05002315"],["dc.identifier.gro","3146679"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4470"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0129-055X"],["dc.title","On the topology of ehBduality"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1751"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Algebraic & Geometric Topology"],["dc.bibliographiccitation.lastpage","1790"],["dc.bibliographiccitation.volume","9"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Schick, Thomas"],["dc.contributor.author","Schröder, Ingo"],["dc.contributor.author","Wiethaup, Moritz"],["dc.date.accessioned","2017-09-07T11:43:05Z"],["dc.date.available","2017-09-07T11:43:05Z"],["dc.date.issued","2009"],["dc.identifier.doi","10.2140/agt.2009.9.1751"],["dc.identifier.gro","3146658"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4446"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.relation.issn","1472-2747"],["dc.title","Landweber exact formal group laws and smooth cohomology theories"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","129"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Homology, Homotopy and Applications"],["dc.bibliographiccitation.lastpage","180"],["dc.bibliographiccitation.volume","10"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Schick, Thomas"],["dc.contributor.author","Spitzweck, Markus"],["dc.date.accessioned","2017-09-07T11:43:11Z"],["dc.date.available","2017-09-07T11:43:11Z"],["dc.date.issued","2008"],["dc.identifier.doi","10.4310/HHA.2008.v10.n1.a6"],["dc.identifier.gro","3146664"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4452"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","1532-0073"],["dc.title","Inertia and delocalized twisted cohomology"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","303"],["dc.bibliographiccitation.lastpage","357"],["dc.bibliographiccitation.seriesnr","17"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Schick, Thomas"],["dc.contributor.editor","Bär, Christian"],["dc.contributor.editor","Lohkamp, Joachim"],["dc.contributor.editor","Schwarz, Matthias"],["dc.date.accessioned","2017-09-07T11:43:05Z"],["dc.date.available","2017-09-07T11:43:05Z"],["dc.date.issued","2011"],["dc.description.abstract","Generalized differential cohomology theories, in particular differential K-theory (often called “smooth K-theory”), are becoming an important tool in differential geometry and in mathematical physics.In this survey, we describe the developments of the recent decades in this area. In particular, we discuss axiomatic characterizations of differential K-theory (and that these uniquely characterize differential K-theory). We describe several explicit constructions, based on vector bundles, on families of differential operators, or using homotopy theory and classifying spaces. We explain the most important properties, in particular about the multiplicative structure and push-forward maps and will state versions of the Riemann–Roch theorem and of Atiyah–Singer family index theorem for differential K-theory."],["dc.identifier.doi","10.1007/978-3-642-22842-1_11"],["dc.identifier.gro","3146643"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4430"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.publisher","Springer"],["dc.publisher.place","Heidelberg"],["dc.relation.crisseries","Springer Proceedings in Mathematics"],["dc.relation.doi","10.1007/978-3-642-22842-1"],["dc.relation.eisbn","978-3-642-22842-1"],["dc.relation.isbn","978-3-642-22841-4"],["dc.relation.ispartof","Global Differential Geometry"],["dc.relation.ispartofseries","Springer Proceedings in Mathematics;17"],["dc.relation.issn","2190-5614"],["dc.title","Differential K-theory: A Survey"],["dc.type","book_chapter"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1027"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Journal of Noncommutative Geometry"],["dc.bibliographiccitation.lastpage","1104"],["dc.bibliographiccitation.volume","7"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Schick, Thomas"],["dc.date.accessioned","2017-09-07T11:43:04Z"],["dc.date.available","2017-09-07T11:43:04Z"],["dc.date.issued","2013"],["dc.description.abstract","We construct differential K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct a push-forward map in differential orbifold K-theory. Finally, we construct a non-degenerate intersection pairing with values in C/Z for the subclass of smooth orbifolds which can be written as global quotients by a finite group action. We construct a real subfunctor of our theory, where the pairing restricts to a non-degenerate R/Z-valued pairing."],["dc.identifier.doi","10.4171/JNCG/143"],["dc.identifier.gro","3146640"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4427"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","1661-6952"],["dc.title","Differential orbifold K-theory"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","227"],["dc.bibliographiccitation.lastpage","347"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Schick, Thomas"],["dc.contributor.author","Spitzweck, Markus"],["dc.contributor.author","Thom, Andreas"],["dc.contributor.editor","Cortiñas, Guillermo"],["dc.contributor.editor","Cuntz, Joachim"],["dc.contributor.editor","Karoubi, Max"],["dc.contributor.editor","Nest, Ryszard"],["dc.contributor.editor","Weibel, Charles A."],["dc.date.accessioned","2017-09-07T11:43:06Z"],["dc.date.available","2017-09-07T11:43:06Z"],["dc.date.issued","2008"],["dc.description.abstract","We extend Pontrjagin duality from topological abelian groups to certain locally compact group stacks. To this end we develop a sheaf theory on the big site of topological spaces S in order to prove that the sheaves ExtiShAbS(G,T), i = 1, 2, vanish, where G is the sheaf represented by a locally compact abelian group and T is the circle. As an application of the theory we interpret topological T-duality of principal Tn-bundles in terms of Pontrjagin duality of abelian group stacks."],["dc.identifier.doi","10.4171/060-1/10"],["dc.identifier.gro","3146659"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4447"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.publisher","European Mathematical Society"],["dc.publisher.place","Zürich"],["dc.relation.eisbn","978-3-03719-560-4"],["dc.relation.isbn","978-3-03719-060-9"],["dc.relation.ispartof","$K$-theory and noncommutative geometry"],["dc.title","Duality for topological abelian group stacks and ehBduality"],["dc.type","book_chapter"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1"],["dc.bibliographiccitation.journal","Annales mathématiques Blaise Pascal"],["dc.bibliographiccitation.lastpage","16"],["dc.bibliographiccitation.volume","17"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Kreck, Matthias"],["dc.contributor.author","Schick, Thomas"],["dc.date.accessioned","2019-07-09T11:53:17Z"],["dc.date.available","2019-07-09T11:53:17Z"],["dc.date.issued","2010"],["dc.description.abstract","In this paper we give a geometric cobordism description of differential integral cohomology. The main motivation to consider this model (for other models see [5, 6, 7, 8]) is that it allows for simple descriptions of both the cup product and the integration. In particular it is very easy to verify the compatibilty of these structures. We proceed in a similar way in the case of differential cobordism as constructed in [4]. There the starting point was Quillen\\’s cobordism description of singular cobordism groups for a differential manifold X. Here we use instead the similar description of integral cohomology from [11]. This cohomology theory is denoted by SH (X). In this description smooth manifolds in Quillen\\’s description are replaced by so-called stratifolds, which are certain stratified spaces. The cohomology theory SH (X) is naturally isomorphic to ordinary integral cohomology H (X), thus we obtain a cobordism type definition of the differential extension of ordinary integral cohomology."],["dc.identifier.doi","10.5802/ambp.276"],["dc.identifier.fs","582332"],["dc.identifier.purl","https://resolver.sub.uni-goettingen.de/purl?gs-1/7241"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/60387"],["dc.language.iso","en"],["dc.notes.intern","Merged from goescholar"],["dc.rights","Goescholar"],["dc.rights.uri","https://goescholar.uni-goettingen.de/licenses"],["dc.title","A geometric description of differential cohomology"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.version","published_version"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","429"],["dc.bibliographiccitation.lastpage","466"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Schick, Thomas"],["dc.contributor.editor","Booβ-Bavnbek , Bernhelm"],["dc.contributor.editor","Klimek, Slawomir"],["dc.contributor.editor","Lesch , Matthias"],["dc.contributor.editor","Zhang, Weiping"],["dc.date.accessioned","2017-09-07T11:47:11Z"],["dc.date.available","2017-09-07T11:47:11Z"],["dc.date.issued","2006"],["dc.identifier.gro","3146677"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4468"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.publisher","World Sci. Publ."],["dc.publisher.place","Hackensack, NJ"],["dc.relation.eisbn","978-981-4478-02-1"],["dc.relation.isbn","978-981-256-805-2"],["dc.relation.ispartof","Analysis, geometry and topology of elliptic operators: Papers in Honor of Krzysztof P Wojciechowski"],["dc.title","hBduality for non-free circle actions"],["dc.type","book_chapter"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1093"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Algebraic & Geometric Topology"],["dc.bibliographiccitation.lastpage","1139"],["dc.bibliographiccitation.volume","8"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Schick, Thomas"],["dc.date.accessioned","2017-09-07T11:43:11Z"],["dc.date.available","2017-09-07T11:43:11Z"],["dc.date.issued","2008"],["dc.identifier.doi","10.2140/agt.2008.8.1093"],["dc.identifier.gro","3146661"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4449"],["dc.notes.intern","mathe"],["dc.notes.status","public"],["dc.notes.submitter","chake"],["dc.relation.issn","1472-2747"],["dc.title","Real secondary index theory"],["dc.type","journal_article"],["dc.type.internalPublication","unknown"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","45"],["dc.bibliographiccitation.issue","328"],["dc.bibliographiccitation.journal","Astérisque"],["dc.bibliographiccitation.lastpage","135"],["dc.contributor.author","Bunke, Ulrich"],["dc.contributor.author","Schick, Thomas"],["dc.date.accessioned","2017-09-07T11:43:08Z"],["dc.date.available","2017-09-07T11:43:08Z"],["dc.date.issued","2009"],["dc.identifier.gro","3146656"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/4443"],["dc.language.iso","en"],["dc.notes.intern","mathe"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0303-1179"],["dc.title","Smooth K-theory"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]