The complex of cycles on a surface (after Bestvina–Bux–Margalit)
نویسنده
چکیده
The complex of cycles on a surface is a cell complex that encodes all the ways that an element of first homology can be written as an embedded cycle. It was introduced by Bestvina–Bux–Margalit and plays an important role in their calculation of the cohomological dimension of the Torelli group. We give a detailed proof that this complex is contractible, expanding upon one of the proofs given by Bestvina–Bux– Margalit.
منابع مشابه
On cyclic branched coverings of prime knots
The Torelli subgroup of Out(Fn) Mladen Bestvina, Utah The group in the title is the kernel of the natural map Out(Fn) –> GLn(Z). As for the classical mapping class group counterparts (except for the work of Mess in low genus), the basic features such as the dimension and finiteness properties are unknown. I will describe an approach to an understanding to these groups that leads to a complete s...
متن کاملThe Cyclic Cycle Complex of a Surface
In a recent preprint, Bestvina, Bux, and Margalit construct a cell complex that gives a combinatorial model for the collection of isotopy classes of oriented curve systems within a given homology class in a closed orientable surface [BBM]. A key property of the complex is that it is contractible. Here we will construct a different complex, this one a simplicial complex rather than a cell comple...
متن کاملKai-uwe Bux
Type FPs A group Γ is of type FPs if Z, regarded as a ZΓ–module via the trivial action, admits a partial projective resolution Ps → Ps−1 → · · · → P1 → P0 → Z→ 0 by finitely generated ZΓ–modules Pi . Every group is of type FP0 . Type FP1 is equivalent to the property of finite generation. Every finitely-presented group is of type FP2 , but Bestvina–Brady showed the converse does not hold in gen...
متن کاملOpen-Hole Size and Thermal Cycling Effects on Mass Loss and Surface Degradation of Polymer Matrix Composites
Degradation is a common problem for polymer matrix composites (PMCs) under low thermal cycling conditions. This paper investigates the effects of low thermal cycling on total mass loss (TML) and surface degradation of PMCs. Unnotched and open-hole specimens were weighed before and after low thermal cycling. The total mass loss and surface degradation of the specimens were studied over 250 cycle...
متن کاملEffects of particles size distribution and occupied area of CdS photosensitizer on photovoltaic performance
Cadmium sulfide (CdS) photosensitizers were successfully formed on the mesoporous titania films using the successive ionic layer adsorption and reaction (SILAR) method in five cycles, and the effects of particles size distribution and their occupied surface area on the morphology, topography, optical property, and photovoltaic performance were investigated. Scanning electron microscope (SEM) im...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015