Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 1 (2015), 169-190.
Oriented orbifold vertex groups and cobordism and an associated differential graded algebra
We develop a homology of vertex groups as a tool for studying orbifolds and orbifold cobordism and its torsion. To a pair of conjugacy classes of degree- and degree- finite subgroups of and we associate the parity with which occurs up to conjugacy as a vertex group in the orbifold . This extends to a map between the vector spaces whose bases are all such conjugacy classes in and then . Using orbifold graphs, we prove is a differential and defines a homology, . We develop a map for a subcomplex of groups which admit orientation-reversing automorphisms. We then look at examples and algebraic properties of and , including that is a derivation. We prove that the natural map between the set of diffeomorphism classes of closed, locally oriented –orbifolds and maps into and that this map is onto for . We relate to orbifold cobordism and surgery and show that quotients to a map between oriented orbifold cobordism and .
Algebr. Geom. Topol., Volume 15, Number 1 (2015), 169-190.
Received: 1 November 2013
Revised: 23 May 2014
Accepted: 21 July 2014
First available in Project Euclid: 16 November 2017
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Druschel, Kimberly. Oriented orbifold vertex groups and cobordism and an associated differential graded algebra. Algebr. Geom. Topol. 15 (2015), no. 1, 169--190. doi:10.2140/agt.2015.15.169. https://projecteuclid.org/euclid.agt/1510840910