Finite groups, spherical 2-categories, and 4-manifold invariants Export

@article{citeulike:1665666, abstract = {In this paper we define a class of state-sum invariants of compact closed oriented piece-wise linear 4-manifolds using finite groups. The definition of these state-sums follows from the general abstract construction of 4-manifold invariants using spherical 2-categories, as we defined in a previous paper, although it requires a slight generalization of that construction. We show that the state-sum invariants of Birmingham and Rakowski, who studied Dijkgraaf-Witten type invariants in dimension 4, are special examples of the general construction that we present in this paper. They showed that their invariants are non-trivial by some explicit computations, so our construction includes interesting examples already. Finally, we indicate how our construction is related to homotopy 3-types. This connection suggests that there are many more interesting examples of our construction to be found in the work on homotopy 3-types, such as by Brown, for example.}, archivePrefix = {arXiv}, author = {Mackaay, M.}, citeulike-article-id = {1665666}, citeulike-linkout-0 = {http://arxiv.org/abs/math/9903003}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/9903003}, citeulike-linkout-2 = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1999math......3003M}, eprint = {math/9903003}, journal = {ArXiv Mathematics e-prints}, keywords = {2-categories, 4-manifolds, invariance}, month = {February}, posted-at = {2007-09-17 12:48:41}, priority = {2}, title = {Finite groups, spherical 2-categories, and 4-manifold invariants}, url = {http://arxiv.org/abs/math/9903003}, year = {1999} }

TY - JOUR ID - citeulike:1665666 L3 - citeulike-article-id:1665666 N2 - In this paper we define a class of state-sum invariants of compact closed oriented piece-wise linear 4-manifolds using finite groups. The definition of these state-sums follows from the general abstract construction of 4-manifold invariants using spherical 2-categories, as we defined in a previous paper, although it requires a slight generalization of that construction. We show that the state-sum invariants of Birmingham and Rakowski, who studied Dijkgraaf-Witten type invariants in dimension 4, are special examples of the general construction that we present in this paper. They showed that their invariants are non-trivial by some explicit computations, so our construction includes interesting examples already. Finally, we indicate how our construction is related to homotopy 3-types. This connection suggests that there are many more interesting examples of our construction to be found in the work on homotopy 3-types, such as by Brown, for example. JF - ArXiv Mathematics e-prints TI - Finite groups, spherical 2-categories, and 4-manifold invariants KW - 2-categories KW - 4-manifolds KW - invariance AU - Mackaay, M PY - 1999/February// UR - http://arxiv.org/abs/math/9903003 ER -