Two-vector bundles define a form of elliptic cohomology Export

@misc{citeulike:1996493, abstract = {We prove that for well-behaved small commutative rig (aka. symmetric bimonoidal) categories R the algebraic K-theory space of the K-theory spectrum, HR, of R is equivalent to K\_0(\pi\_0R)\times |BGL(R)|^+ where GL(R) is the monoidal category of weakly invertible matrices over R. In particular, this proves the conjecture of Baas-Dundas-Rognes that K(ku) is the K-theory of the 2-category of complex 2-vector spaces. Hence, the work of the fourth author and Christian Ausoni on K(ku) shows that the theory of virtual 2-vector bundles as in Baas-Dundas-Rognes qualifies as a form of elliptic cohomology theory.}, archivePrefix = {arXiv}, author = {Baas, Nils A. and Dundas, Bjorn I. and Richter, Birgit and Rognes, John}, citeulike-article-id = {1996493}, citeulike-linkout-0 = {http://arxiv.org/abs/0706.0531}, citeulike-linkout-1 = {http://arxiv.org/pdf/0706.0531}, day = {4}, eprint = {0706.0531}, keywords = {ellhom, k-theory}, month = {Jun}, posted-at = {2007-11-27 20:09:50}, priority = {2}, title = {Two-vector bundles define a form of elliptic cohomology}, url = {http://arxiv.org/abs/0706.0531}, year = {2007} }

TY - ELEC ID - citeulike:1996493 L3 - citeulike-article-id:1996493 N2 - We prove that for well-behaved small commutative rig (aka. symmetric bimonoidal) categories R the algebraic K-theory space of the K-theory spectrum, HR, of R is equivalent to K_0(\pi_0R)\times |BGL(R)|^+ where GL(R) is the monoidal category of weakly invertible matrices over R. In particular, this proves the conjecture of Baas-Dundas-Rognes that K(ku) is the K-theory of the 2-category of complex 2-vector spaces. Hence, the work of the fourth author and Christian Ausoni on K(ku) shows that the theory of virtual 2-vector bundles as in Baas-Dundas-Rognes qualifies as a form of elliptic cohomology theory. TI - Two-vector bundles define a form of elliptic cohomology KW - ellhom KW - k-theory AU - Baas, Nils AU - Dundas, Bjorn AU - Richter, Birgit AU - Rognes, John PY - 2007/Jun/04/ UR - http://arxiv.org/abs/0706.0531 ER -