Mathematics and Computer ScienceCopyright (c) 2020 John Carroll University All rights reserved.
https://collected.jcu.edu/math_cs-facpub
Recent documents in Mathematics and Computer Scienceen-usFri, 24 Jan 2020 06:40:14 PST3600Discrete Groups and the Complex Contact Geometry of SL(2, C)
https://collected.jcu.edu/math_cs-facpub/5
https://collected.jcu.edu/math_cs-facpub/5Fri, 02 Nov 2012 15:58:53 PDT
We investigate the vertical foliation of the standard complex contact structure on Γ \ Sl(2, C), where Γ is a discrete subgroup. We find that, if Γ is nonelementary, the vertical leaves on Γ \ Sl(2, C) are holomorphic but not regular. However, if Γ is Kleinian, then Γ \ Sl(2, C) contains an open, dense set on which the vertical leaves are regular, complete and biholomorphic to C ∗. If Γ is a uniform lattice, the foliation is nowhere regular, although there are both infinitely many compact and infinitely many nonclosed leaves.
]]>
Brendan ForemanIsometries Homotopic to the Identity
https://collected.jcu.edu/math_cs-facpub/4
https://collected.jcu.edu/math_cs-facpub/4Fri, 02 Nov 2012 15:58:52 PDT
The types of surfaces which admit nontrivial isometries homotopic to the identity are classified up to diffeomorphism. In dimension three this is done for complete manifolds of constant negative curvature. Three-dimensional visibility manifolds that admit nontrivial isometries homotopic to the identity are shown to be diffeomorphic to a product L x RI.
]]>
Douglas A. NorrisOdd Primary Periodic Phenomena in the Classical Adams Spectral Sequence
https://collected.jcu.edu/math_cs-facpub/3
https://collected.jcu.edu/math_cs-facpub/3Fri, 02 Nov 2012 15:58:52 PDT
We study certain periodic phenomena in the cohomology of the mod ρ Steenrod algebra which are related to the polynomial generators υ_{n} ∈ π∗ΒΡ. A chromatic resolution of the Ε_{2} term of the classical Adams spectral sequence is constructed.
]]>
Paul L. ShickOn Root Invariants of Periodic Classes in Exta(Z/2,Z/2)
https://collected.jcu.edu/math_cs-facpub/2
https://collected.jcu.edu/math_cs-facpub/2Fri, 02 Nov 2012 15:58:50 PDT
We prove that if a class in the cohomology of the mod 2 Steenrod algebra is υ_{n}-periodic in the sense of [10[, then its root invariant must be υ_{n+1}-periodic, where υ_{n} denotes the nth generator of π∗(ΒΡ).
]]>
Paul L. ShickPeriodic Phenomena in the Classical Adams Spectral Sequence
https://collected.jcu.edu/math_cs-facpub/1
https://collected.jcu.edu/math_cs-facpub/1Fri, 02 Nov 2012 15:58:50 PDT
We investigate certain periodic phenomena in the classical Adams spectral sequence which are related to the polynomial generators υ_{n} in π∗(ΒΡ). We define the notion of a class α in Ext_{Α}(Ζ/2,Ζ/2) being υ_{n}-periodic or υ_{n}-torsion and prove that classes that are υ_{n}-torsion are also υ_{κ}-torsion for all κ such that 0 ≤ κ ≤ n. This allows us to define a chromatic filtration of Ext_{Α}(Ζ/2,Ζ/2) paralleling the chromatic filtration of the Novikov spectral sequence Ε_{2}-term given in [13].
]]>
Mark Mahowald et al.