التفاصيل البيبلوغرافية
| العنوان: |
Generalized manifolds, normal invariants, and $\mathbb{L}$-homology |
| المؤلفون: |
Hegenbarth, Friedrich, Repovš, Dušan D. |
| المصدر: |
Proc. Edinb. Math. Soc. (2) 64:3 (2021), 574-589 |
| سنة النشر: |
2021 |
| مصطلحات موضوعية: |
Mathematics - Algebraic Topology, Mathematics - Geometric Topology, Primary: 55N07, 55R20, 57P10, 57R67, Secondary: 18F15, 55M05, 55N20, 57P05, 57P99, 57R65 |
| الوصف: |
Let $X^{n}$ be an arbitrary oriented closed generalized $n$-manifold, $n\ge 5$. In our recent paper (Proc. Edinb. Math. Soc. (2) 63 (2020), no. 2, 597-607) we have constructed a map $t:\mathcal{N}(X^{n}) \to H^{st}_{n} ( X^{n}; \mathbb{L}^+)$ which extends the normal invariant map for the case when $X^{n}$ is a topological $n$-manifold. Here, $\mathcal{N}(X^{n})$ denotes the set of all normal bordism classes of degree one normal maps $(f,b): M^{n} \to X^{n},$ and $H^{st}_{*} ( X^{n}; \mathbb{E})$ denotes the Steenrod homology of the spectrum $\mathbb{E}$. An important nontrivial question arose whether the map $t$ is bijective (note that this holds in the case that $X^{n}$ is a topological $n$-manifold). It is the purpose of this paper to prove that the answer to this question is affirmative. |
| نوع الوثيقة: |
Working Paper |
| DOI: |
10.1017/S0013091521000316 |
| URL الوصول: |
http://arxiv.org/abs/2110.12742 |
| رقم الانضمام: |
edsarx.2110.12742 |
| قاعدة البيانات: |
arXiv |