Spherical Milnor Spaces II: Projective Quotients and Higher Topological Structures
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913133584449536 |
|---|---|
| author | Magnot, Jean-Pierre |
| author_facet | Magnot, Jean-Pierre |
| contents | We introduce a spherical variant of Milnor's classifying construction for diffeological groups, based on quadratic normalization of barycentric coordinates. This construction gives rise to a contractible diffeological space endowed with commuting actions of a group $G$ and of $\mathbb{Z}_2$, leading naturally to a hierarchy of quotient spaces.
We investigate the topological and geometric properties of these quotients, including a projective model and a double quotient space which encodes twisted and higher structures. In particular, we show that this framework provides a natural setting for the study of principal bundles with $\mathbb{Z}_2$-twists, and leads to obstruction classes in low-degree cohomology.
The construction is further related to non-abelian gerbes and higher bundles, providing a bridge between diffeological geometry, classifying space theory, and higher topological structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16370 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spherical Milnor Spaces II: Projective Quotients and Higher Topological Structures Magnot, Jean-Pierre Differential Geometry Algebraic Geometry 55R10, 57R20, 58B25, 53C27 We introduce a spherical variant of Milnor's classifying construction for diffeological groups, based on quadratic normalization of barycentric coordinates. This construction gives rise to a contractible diffeological space endowed with commuting actions of a group $G$ and of $\mathbb{Z}_2$, leading naturally to a hierarchy of quotient spaces. We investigate the topological and geometric properties of these quotients, including a projective model and a double quotient space which encodes twisted and higher structures. In particular, we show that this framework provides a natural setting for the study of principal bundles with $\mathbb{Z}_2$-twists, and leads to obstruction classes in low-degree cohomology. The construction is further related to non-abelian gerbes and higher bundles, providing a bridge between diffeological geometry, classifying space theory, and higher topological structures. |
| title | Spherical Milnor Spaces II: Projective Quotients and Higher Topological Structures |
| topic | Differential Geometry Algebraic Geometry 55R10, 57R20, 58B25, 53C27 |
| url | https://arxiv.org/abs/2605.16370 |